MathDB

2^n does not divide a^k+b^k+c^k

Source: 2009 Peru Iberoamerican TST problem 5

May 9, 2023

number theory

Problem Statement

Let

a, b, c

be positive integers whose greatest common divisor is

1

. Determine whether there always exists a positive integer

n

such that, for every positive integer

k

, the number

2^n

is not a divisor of

a^k+b^k+c^k