8

Part of 1993 Poland - First Round

Problems(1)

When is (a+b+c)^13 divisible by abc?

Source: Poland Math Olympiad 1993 Round 1 #8

Given positive integers

a,b,c

(a+b+c)^{13}

is divisible by

b

b^3

is divisible by

c

c^3

is divisible by

a

(a+b+c)^{13}

is divisible by

abc