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Quadruples (a,b,x,y) such that n= ax+by, and a>b

Source: 2023 Girls in Mathematics Tournament- Level B, Problem 2

October 29, 2023
algebranumber theory

Problem Statement

Given nn a positive integer, define TnT_n the number of quadruples of positive integers (a,b,x,y)(a,b,x,y) such that a>ba>b and n=ax+byn= ax+by. Prove that T2023T_{2023} is odd.
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