19

Part of 2016 Latvia Baltic Way TST

Problems(1)

x^{2015} + y^{2015} = z^{2016}, diophantine

Source: 2016 Latvia BW TST P19

Prove that for equation

x^{2015} + y^{2015} = z^{2016}

there are infinitely many solutions where

x,y

z

are different natural numbers.

number theoryDiophantine equationdiophantine