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7^{n-1} - 3^{n-1} is divisible by n, non prime n

Source: 2015 Saudi Arabia BMO TST II p4

July 24, 2020
dividesdivisiblenumber theory

Problem Statement

Prove that there exist infinitely many non prime positive integers nn such that 7n13n17^{n-1} - 3^{n-1} is divisible by nn.
Lê Anh Vinh