2

Part of 2007 Switzerland - Final Round

Problems(1)

a^{2007}+b^{2007}+c^{2007}+2 x 2007abc is divisible by 13

Source: Switzerland - 2007 Swiss MO Final Round p2

a, b, c

be three integers such that

a + b + c

is divisible by

13

a^{2007}+b^{2007}+c^{2007}+2 \cdot 2007abc

is divisible by

13

number theorydividesdivisible