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x^2 + ax + b = 167 y, 1<=a,b<=2004 , no of ordered solutions (a,b)

Source: Singapore Open Math Olympiad 2004 2nd Round p2 SMO

April 3, 2020
number theorydiophantineDiophantine equation

Problem Statement

Find the number of ordered pairs (a,b)(a, b) of integers, where 1≤a,b≤20041 \le a, b \le 2004, such that x2+ax+b=167yx^2 + ax + b = 167 y has integer solutions in xx and yy. Justify your answer.
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