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Residues

Source: Korean National Olympiad 2nd Round 2019 #3

November 16, 2019
number theory

Problem Statement

Suppose that positive integers m,n,km,n,k satisfy the equations m2+1=2n2,2m2+1=11k2.m^2+1=2n^2, 2m^2+1=11k^2. Find the residue when nn is divided by 1717.
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