At first N = p * q, let's find this prime numbers p and q.
Now we have x * x = x mod N.
x * x - x = 0 mod N
x * (x - 1) = 0 mod N
Let's note that x != pq, because x < n. That means x mod p = 0, x - 1 mod q = 0 or x mod q = 0, x - 1 mod p = 0.
Consider {
x mod p = 0
x mod q = 1
}
another case is symmetrical.
x = k * p, because x mod p = 0.
Now we have k * p mod q = 1
k = 1 / p mod q
k = p ^ (-1) mod q
Use Fermat's little theorem k = p ^ (q - 2) mod q.
We find x = k * p, problem is solved.

I have wrong answer on test 2, but all tests that I checked have right answer. Please, give me some tests to check my code.

O(k*(sqrt(n)/log(n) + log(n))).
hint: precalc primes table(so, we can factorize number using O(sqrt(N)/log(N)) operations).
gl.

0 and 1 is trivial solution.
Let x solution it must satisfy for follow requirements:
{x=0(mod p);x=1(mod q);} or
{x=0(mod q);x=1(mod p);}
We can find 2 solution for these equation let it be x1,x2;
And all solution will satisyf for follow requirements (x1+lcm(p,q))mod n,(x2+lcm(p,q))mod n;
but lcm(p,q)==n we have only for solutions
0 1 x1 x2;
Sorry for bad English!

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Problem {

    public static int[] gcd(int a,int b){
        if(a==0){
            return new int[]{0,1};
        }
        int[] w=gcd(b%a,a);
        int x=(w[1]-(b/a)*w[0]);
        int y=w[0];
        return new int[]{x,y};
    }

    public static int[] a = new int[]{2,3,5,7,11,13,17,19,23,29,
31,37,41,43,47,53,59,61,67,71,
73,79,83,89,97,101,103,107,109,113,
127,131,137,139,149,151,157,163,167,173,
179,181,191,193,197,199,211,223,227,229,
233,239,241,251,257,263,269,271,277,281,
283,293,307,311,313,317,331,337,347,349,
353,359,367,373,379,383,389,397,401,409,
419,421,431,433,439,443,449,457,461,463,
467,479,487,491,499,503,509,521,523,541,
547,557,563,569,571,577,587,593,599,601,
607,613,617,619,631,641,643,647,653,659,
661,673,677,683,691,701,709,719,727,733,
739,743,751,757,761,769,773,787,797,809,
811,821,823,827,829,839,853,857,859,863,
877,881,883,887,907,911,919,929,937,941,
947,953,967,971,977,983,991,997,1009,1013,
1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,
1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,
1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,
1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,
1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,
1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,
1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,
1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,
1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,
1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,
1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,
1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,
1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,
1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,
2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,
2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,
2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,
2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,
2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,
2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,
2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,
2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,
2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,
2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,
2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,
2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,
3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,
3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,
3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,
3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,
3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,
3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,
3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,
3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,
3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,
3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,
3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,
3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,
4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,
4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,
4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,
4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,
4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,
4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,
4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,
4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,
4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,
4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,
4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,
4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,
5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,
5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,
5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,
5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,
5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,
5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,
5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,
5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,
5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,
5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,
5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,
5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,
6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,
6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,
6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,
6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,
6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,
6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,
6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,
6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,
6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,
6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,
6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,
7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,
7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,
7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,
7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,
7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,
7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,
7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,
7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,
7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,
7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,
7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,
8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,
8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,
8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,
8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,
8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,
8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,
8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,
8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,
8747,8753,8761,8779,8783,8803,8807,8819,8821,8831,
8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,
8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,
9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,
9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,
9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,
9293,9311,9319,9323,9337,9341,9343,9349,9371,9377,
9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,
9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,
9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,
9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,
9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,
9817,9829,9833,9839,9851,9857,9859,9871,9883,9887,
9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,
10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,
10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,
10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,
10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,
10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,
10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,
10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,
10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,
10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,
10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,
10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,
11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,
11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,
11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,
11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,
11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,
11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,
11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,
11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,
11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,
11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,
12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,
12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,
12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,
12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,
12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,
12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,
12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,
12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,
12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,
12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,
12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,
13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,
13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,
13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,
13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,
13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,
13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,
13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,
13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,
13789,13799,13807,13829,13831,13841,13859,13873,13877,13879,
13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,
13997,13999,14009,14011,14029,14033,14051,14057,14071,14081,
14083,14087,14107,14143,14149,14153,14159,14173,14177,14197,
14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,
14327,14341,14347,14369,14387,14389,14401,14407,14411,14419,
14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,
14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,
14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,
14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,
14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,
14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,
14951,14957,14969,14983,15013,15017,15031,15053,15061,15073,
15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,
15161,15173,15187,15193,15199,15217,15227,15233,15241,15259,
15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,
15329,15331,15349,15359,15361,15373,15377,15383,15391,15401,
15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,
15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,
15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,
15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,
15787,15791,15797,15803,15809,15817,15823,15859,15877,15881,
15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,
15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,
16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,
16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,
16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,
16411,16417,16421,16427,16433,16447,16451,16453,16477,16481,
16487,16493,16519,16529,16547,16553,16561,16567,16573,16603,
16607,16619,16631,16633,16649,16651,16657,16661,16673,16691,
16693,16699,16703,16729,16741,16747,16759,16763,16787,16811,
16823,16829,16831,16843,16871,16879,16883,16889,16901,16903,
16921,16927,16931,16937,16943,16963,16979,16981,16987,16993,
17011,17021,17027,17029,17033,17041,17047,17053,17077,17093,
17099,17107,17117,17123,17137,17159,17167,17183,17189,17191,
17203,17207,17209,17231,17239,17257,17291,17293,17299,17317,
17321,17327,17333,17341,17351,17359,17377,17383,17387,17389,
17393,17401,17417,17419,17431,17443,17449,17467,17471,17477,
17483,17489,17491,17497,17509,17519,17539,17551,17569,17573,
17579,17581,17597,17599,17609,17623,17627,17657,17659,17669,
17681,17683,17707,17713,17729,17737,17747,17749,17761,17783,
17789,17791,17807,17827,17837,17839,17851,17863,17881,17891,
17903,17909,17911,17921,17923,17929,17939,17957,17959,17971,
17977,17981,17987,17989,18013,18041,18043,18047,18049,18059,
18061,18077,18089,18097,18119,18121,18127,18131,18133,18143,
18149,18169,18181,18191,18199,18211,18217,18223,18229,18233,
18251,18253,18257,18269,18287,18289,18301,18307,18311,18313,
18329,18341,18353,18367,18371,18379,18397,18401,18413,18427,
18433,18439,18443,18451,18457,18461,18481,18493,18503,18517,
18521,18523,18539,18541,18553,18583,18587,18593,18617,18637,
18661,18671,18679,18691,18701,18713,18719,18731,18743,18749,
18757,18773,18787,18793,18797,18803,18839,18859,18869,18899,
18911,18913,18917,18919,18947,18959,18973,18979,19001,19009,
19013,19031,19037,19051,19069,19073,19079,19081,19087,19121,
19139,19141,19157,19163,19181,19183,19207,19211,19213,19219,
19231,19237,19249,19259,19267,19273,19289,19301,19309,19319,
19333,19373,19379,19381,19387,19391,19403,19417,19421,19423,
19427,19429,19433,19441,19447,19457,19463,19469,19471,19477,
19483,19489,19501,19507,19531,19541,19543,19553,19559,19571,
19577,19583,19597,19603,19609,19661,19681,19687,19697,19699,
19709,19717,19727,19739,19751,19753,19759,19763,19777,19793,
19801,19813,19819,19841,19843,19853,19861,19867,19889,19891,
19913,19919,19927,19937,19949,19961,19963,19973,19979,19991,
19993,19997,20011,20021,20023,20029,20047,20051,20063,20071,
20089,20101,20107,20113,20117,20123,20129,20143,20147,20149,
20161,20173,20177,20183,20201,20219,20231,20233,20249,20261,
20269,20287,20297,20323,20327,20333,20341,20347,20353,20357,
20359,20369,20389,20393,20399,20407,20411,20431,20441,20443,
20477,20479,20483,20507,20509,20521,20533,20543,20549,20551,
20563,20593,20599,20611,20627,20639,20641,20663,20681,20693,
20707,20717,20719,20731,20743,20747,20749,20753,20759,20771,
20773,20789,20807,20809,20849,20857,20873,20879,20887,20897,
20899,20903,20921,20929,20939,20947,20959,20963,20981,20983,
21001,21011,21013,21017,21019,21023,21031,21059,21061,21067,
21089,21101,21107,21121,21139,21143,21149,21157,21163,21169,
21179,21187,21191,21193,21211,21221,21227,21247,21269,21277,
21283,21313,21317,21319,21323,21341,21347,21377,21379,21383,
21391,21397,21401,21407,21419,21433,21467,21481,21487,21491,
21493,21499,21503,21517,21521,21523,21529,21557,21559,21563,
21569,21577,21587,21589,21599,21601,21611,21613,21617,21647,
21649,21661,21673,21683,21701,21713,21727,21737,21739,21751,
21757,21767,21773,21787,21799,21803,21817,21821,21839,21841,
21851,21859,21863,21871,21881,21893,21911,21929,21937,21943,
21961,21977,21991,21997,22003,22013,22027,22031,22037,22039,
22051,22063,22067,22073,22079,22091,22093,22109,22111,22123,
22129,22133,22147,22153,22157,22159,22171,22189,22193,22229,
22247,22259,22271,22273,22277,22279,22283,22291,22303,22307,
22343,22349,22367,22369,22381,22391,22397,22409,22433,22441,
22447,22453,22469,22481,22483,22501,22511,22531,22541,22543,
22549,22567,22571,22573,22613,22619,22621,22637,22639,22643,
22651,22669,22679,22691,22697,22699,22709,22717,22721,22727,
22739,22741,22751,22769,22777,22783,22787,22807,22811,22817,
22853,22859,22861,22871,22877,22901,22907,22921,22937,22943,
22961,22963,22973,22993,23003,23011,23017,23021,23027,23029,
23039,23041,23053,23057,23059,23063,23071,23081,23087,23099,
23117,23131,23143,23159,23167,23173,23189,23197,23201,23203,
23209,23227,23251,23269,23279,23291,23293,23297,23311,23321,
23327,23333,23339,23357,23369,23371,23399,23417,23431,23447,
23459,23473,23497,23509,23531,23537,23539,23549,23557,23561,
23563,23567,23581,23593,23599,23603,23609,23623,23627,23629,
23633,23663,23669,23671,23677,23687,23689,23719,23741,23743,
23747,23753,23761,23767,23773,23789,23801,23813,23819,23827,
23831,23833,23857,23869,23873,23879,23887,23893,23899,23909,
23911,23917,23929,23957,23971,23977,23981,23993,24001,24007,
24019,24023,24029,24043,24049,24061,24071,24077,24083,24091,
24097,24103,24107,24109,24113,24121,24133,24137,24151,24169,
24179,24181,24197,24203,24223,24229,24239,24247,24251,24281,
24317,24329,24337,24359,24371,24373,24379,24391,24407,24413,
24419,24421,24439,24443,24469,24473,24481,24499,24509,24517,
24527,24533,24547,24551,24571,24593,24611,24623,24631,24659,
24671,24677,24683,24691,24697,24709,24733,24749,24763,24767,
24781,24793,24799,24809,24821,24841,24847,24851,24859,24877,
24889,24907,24917,24919,24923,24943,24953,24967,24971,24977,
24979,24989,25013,25031,25033,25037,25057,25073,25087,25097,
25111,25117,25121,25127,25147,25153,25163,25169,25171,25183,
25189,25219,25229,25237,25243,25247,25253,25261,25301,25303,
25307,25309,25321,25339,25343,25349,25357,25367,25373,25391,
25409,25411,25423,25439,25447,25453,25457,25463,25469,25471,
25523,25537,25541,25561,25577,25579,25583,25589,25601,25603,
25609,25621,25633,25639,25643,25657,25667,25673,25679,25693,
25703,25717,25733,25741,25747,25759,25763,25771,25793,25799,
25801,25819,25841,25847,25849,25867,25873,25889,25903,25913,
25919,25931,25933,25939,25943,25951,25969,25981,25997,25999,
26003,26017,26021,26029,26041,26053,26083,26099,26107,26111,
26113,26119,26141,26153,26161,26171,26177,26183,26189,26203,
26209,26227,26237,26249,26251,26261,26263,26267,26293,26297,
26309,26317,26321,26339,26347,26357,26371,26387,26393,26399,
26407,26417,26423,26431,26437,26449,26459,26479,26489,26497,
26501,26513,26539,26557,26561,26573,26591,26597,26627,26633,
26641,26647,26669,26681,26683,26687,26693,26699,26701,26711,
26713,26717,26723,26729,26731,26737,26759,26777,26783,26801,
26813,26821,26833,26839,26849,26861,26863,26879,26881,26891,
26893,26903,26921,26927,26947,26951,26953,26959,26981,26987,
26993,27011,27017,27031,27043,27059,27061,27067,27073,27077,
27091,27103,27107,27109,27127,27143,27179,27191,27197,27211,
27239,27241,27253,27259,27271,27277,27281,27283,27299,27329,
27337,27361,27367,27397,27407,27409,27427,27431,27437,27449,
27457,27479,27481,27487,27509,27527,27529,27539,27541,27551,
27581,27583,27611,27617,27631,27647,27653,27673,27689,27691,
27697,27701,27733,27737,27739,27743,27749,27751,27763,27767,
27773,27779,27791,27793,27799,27803,27809,27817,27823,27827,
27847,27851,27883,27893,27901,27917,27919,27941,27943,27947,
27953,27961,27967,27983,27997,28001,28019,28027,28031,28051,
28057,28069,28081,28087,28097,28099,28109,28111,28123,28151,
28163,28181,28183,28201,28211,28219,28229,28277,28279,28283,
28289,28297,28307,28309,28319,28349,28351,28387,28393,28403,
28409,28411,28429,28433,28439,28447,28463,28477,28493,28499,
28513,28517,28537,28541,28547,28549,28559,28571,28573,28579,
28591,28597,28603,28607,28619,28621,28627,28631,28643,28649,
28657,28661,28663,28669,28687,28697,28703,28711,28723,28729,
28751,28753,28759,28771,28789,28793,28807,28813,28817,28837,
28843,28859,28867,28871,28879,28901,28909,28921,28927,28933,
28949,28961,28979,29009,29017,29021,29023,29027,29033,29059,
29063,29077,29101,29123,29129,29131,29137,29147,29153,29167,
29173,29179,29191,29201,29207,29209,29221,29231,29243,29251,
29269,29287,29297,29303,29311,29327,29333,29339,29347,29363,
29383,29387,29389,29399,29401,29411,29423,29429,29437,29443,
29453,29473,29483,29501,29527,29531,29537,29567,29569,29573,
29581,29587,29599,29611,29629,29633,29641,29663,29669,29671,
29683,29717,29723,29741,29753,29759,29761,29789,29803,29819,
29833,29837,29851,29863,29867,29873,29879,29881,29917,29921,
29927,29947,29959,29983,29989,30011,30013,30029,30047,30059,
30071,30089,30091,30097,30103,30109,30113,30119,30133,30137,
30139,30161,30169,30181,30187,30197,30203,30211,30223,30241,
30253,30259,30269,30271,30293,30307,30313,30319,30323,30341,
30347,30367,30389,30391,30403,30427,30431,30449,30467,30469,
30491,30493,30497,30509,30517,30529,30539,30553,30557,30559,
30577,30593,30631,30637,30643,30649,30661,30671,30677,30689,
30697,30703,30707,30713,30727,30757,30763,30773,30781,30803,
30809,30817,30829,30839,30841,30851,30853,30859,30869,30871,
30881,30893,30911,30931,30937,30941,30949,30971,30977,30983,
31013,31019,31033,31039,31051,31063,31069,31079,31081,31091,
31121,31123,31139,31147,31151,31153,31159,31177,31181,31183,
31189,31193,31219,31223,31231,31237,31247,31249,31253,31259,
31267,31271,31277,31307,31319,31321,31327,31333,31337,31357,
31379,31387,31391,31393,31397,31469,31477,31481,31489,31511,
31513,31517,31531,31541,31543,31547,31567,31573,31583,31601,
31607};

    public static void main (String[] args) {
        try {

            Scanner in = new Scanner(System.in);

            Vector<Integer> u = new Vector<Integer>();

            int k=in.nextInt();

            int n=0,p=0,q=0,g=0,x=0,y=0;

            for(int i=0;i<k;i++){

                n=in.nextInt();
                for(int j=0;a[j]<=Math.sqrt(n);j++){
                    if(n%a[j]==0){
                        p=a[j];
                        q=n/a[j];
                        break;
                    }
                }
                int[] w=gcd(p,q);
                u.add(0);
                u.add(1);
                if(w[0]>0){
                    x=p*w[0];
                }else{
                    x=q*w[1];
                }
                x%=n;
                if(x<n+1-x){
                    u.add(x);
                    u.add(n+1-x);
                }else{
                    u.add(n+1-x);
                    u.add(x);
                }
                for(int j=0;j<u.size();j++){
                    System.out.print(u.elementAt(j)+" ");
                }
                System.out.println();
                u = new Vector<Integer>();
            }

        } catch (Exception ex) {

            System.out.println(ex.toString());
        }
    }
}

Is this time normal or there is faster algorithm? I used trivial search for primes p and q, solved k1*p+k2*q=1 by analog of Euqlid algorithm and assume idemponets are 0, 1, k1*p (where k1*p is positive) and n+1-k1*p.

Make a table of first 3401 primes to factor n; use BigInteger.modInverse instead of coding extended GCD algorithm.

I'm really anxious about it.
I do not really understand problem...
What means x*x = x (mod n). What theese brackets mean?

Example:
6                   0 1 3 4
4*4=4%6????
16=4?????????????????????????????

please, help me.
Thanks anyway.

My program is getting TL(1.031) on test 2. Tell me plz what the numbers there are.

What does it mean? An why can it be? Here is my error code

[code deleted]

Edited by moderator 11.07.2006 23:05

I am getting output limit exceeded. Can you help me? here is my program:
var
a,b,c,d,i,k,j:integer;
p:boolean;
s:array[1..1000] of integer;
begin
readln(i);
for a:=1 to i do
readln(s[a]);
for k:=1 to i do begin
if k<>1 then writeln(' ');
write(0,' ',1);
p:=false;
if s[k] mod 2=0 then begin
a:=2; b:=trunc(s[k]/2); p:=true; end;
d:=3;
while p=false do
if (s[i] mod d)=0 then begin a:=d; b:=trunc(s[k]/d); p:=true; end
else d:=d+2;
c:=a;
while c+1<s[i] do begin
if (c-1) mod b=0 then write(' ',c);
if (c+1) mod b=0 then write(' ',c+1);
c:=c+a;
end; end;
end.

I have received AC at time 0.85sec, but my program executed about 40sec on next test:

INPUT
100
for i:=1 to 100 do
writeln(9699690*i);

What is the optimal complexity of this problem?

We are asked to find x, that x*x-x delitsa na N, N-proizvedenie dvuh prostih 4isel. Gde i o6ibaus, WA na vtorom teste

you have to find
x*p+y*q=1 (p,q - primes)
this is possible with extended GCD:
try this:
http://www.brainyencyclopedia.com/encyclopedia/e/ex/extended_euclidean_algorithm.html

My algorithm based on Primes Table and Euclid's Gcd got AC in 0.14sec.But I think it is a little slow.
Maybe someone will have a better solution.If so, could you write is out? Thanks!