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Diophantic equations

Source: Cono Sur Olympiad 2016, problem 2

August 18, 2017
number theorycono sur

Problem Statement

For every k=1,2,…k= 1,2, \ldots let sks_k be the number of pairs (x,y)(x,y) satisfying the equation kx+(k+1)y=1001−kkx + (k+1)y = 1001 - k with xx, yy non-negative integers. Find s1+s2+⋯+s200s_1 + s_2 + \cdots + s_{200}.
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