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3n+1 , 4n+1 are perfect squares then n is divisible by 56

Source: 1997 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p4

January 27, 2020
number theoryPerfect SquaresPerfect Squaredivisible

Problem Statement

Prove that if nn is a natural number such that both 3n+13n+1 and 4n+14n+1 are squares, then nn is divisible by 5656.
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