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n+1 is divisible by 5 , 2^n + n and 2^n -1 are coprime

Source: Irish MO 2017 paper 2 problem 1

December 12, 2022

coprimedivisiblenumber theory

Problem Statement

Does there exist an even positive integer

n

for which

n+1

is divisible by

5

and the two numbers

2^n + n

and

2^n -1

are co-prime?