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Part of 2016 Grand Duchy of Lithuania

Problems(1)

7^n -1 is divisible by 6^n -1

Source: 2016 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

10/3/2020
Determine all positive integers nn such that 7n−17^n -1 is divisible by 6n−16^n -1.
dividesdivisiblenumber theory