P5

Part of 2009 Peru Iberoamerican Team Selection Test

Problems(1)

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

Source: 2009 Peru Iberoamerican TST problem 5

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

2^n

is not a divisor of

a^k+b^k+c^k