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smallest N so that (x^2 -1)(y^2 -1)=N has at least two pairs (x,y) of solutions

Source: Irmo 2013 p2 q8

September 15, 2018
number theoryDiophantine equationDivisors

Problem Statement

Find the smallest positive integer NN for which the equation (x2−1)(y2−1)=N(x^2 -1)(y^2 -1)=N is satis ed by at least two pairs of integers (x,y)(x, y) with 1<x≤y1 < x \le y.
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