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ax+y ranges mod 37

Source: CMO 2022 P3

December 21, 2021
number theory

Problem Statement

Find all positive integers aa such that there exists a set XX of 66 integers satisfying the following conditions: for every k=1,2,…,36k=1,2,\ldots ,36 there exist x,y∈Xx,y\in X such that ax+y−kax+y-k is divisible by 3737.
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