x[i] - y[i] = a * i + b

x[i-1] - y[i-1] = a * (i-1) + b

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x[i] - x[i-1]  - ( y [i] - y[i-1] ) = a



Let x1[i] = x[i] - x[i-1], i > 0. and y1[i] = y[i] - y[i-1], for i>0.


so ,

x1[i] - y1[i] = a,  a = x1[0] - y1[0].

x1[i-1] - y1[i-1] = a
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x1[i]  - x1[i-1] - (y1[i ] - y1[i-1]) = 0  or,

x1[i] - x1[i-1] = y1[i] - y1[i-1]

Let x2[i] = x1[i] - x1[i-1] = x[i] - 2*x[i-1] + x[i-2], for i>1. and
    y2[i] = y1[i] - y1[i-1] = y[i] - 2*y[i-1] + y[i-2], for i>1.

so  x2[i] = y2[i],  for all 1 < i <= n.

Use KMP.

I didn't try this, yet ).