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Pell's Equation Looking Equation

Source: 2015 Korean Mathematical Olmpiad P1, 2015 Korean Junior MO P2

November 1, 2015
number theory

Problem Statement

For a positive integer mm, prove that the number of pairs of positive integers (x,y)(x,y) which satisfies the following two conditions is even or 00.
(i): x2−3y2+2=16mx^2-3y^2+2=16m
(ii): 2y≤x−12y \le x-1
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