10.7

Part of 2010 All-Russian Olympiad Regional Round

Problems(1)

a^{13}+b^{13}+c^{13}=d^2, a+b+c=0

Source: Russian Regional Olympiad 2010 10.7

Are there three pairwise distinct non-zero integers whose sum is zero and whose sum of thirteenth powers is the square of some natural number?

number theoryPerfect Square