11.7

Part of 2009 All-Russian Olympiad Regional Round

Problems(1)

Sum of all 3 perfect powers not divisible by a power of 2

Source: Problem 7 of Russian Regional Olympiad 2009 Grade 11

a

b

c

are positive integers with

\textrm{gcd}(a,b,c)=1

. Is it true that there exist a positive integer

n

a^k+b^k+c^k

is not divisible by

2^n

k

number theorygreatest common divisornumber theory proposed