Question

Prove that there has to be a common prime factor for the following expression to be true (or provide a counter-example):

A^x + B^y = C^z

Answer 1

hmm


1⁴+2³=3²
or
1+8=9
9=9
true
no common factor except 1 (but if we count 1, ther is no way we can get something with a common prime factor since all numbers have factor of 1)


counter example is
1⁴+2³=3²