I want to find some information about how to solve this problem but I don't even know what topic is this. Maybe it's related to symmetric functions. I've tried searching in books but nothing similar found. I will be glad for any kind of help. Thanks.
PROBLEM:
Let $$f_m = \frac{1}{m} \{((x-y)(z-t))^m + ((x-z)(y-t))^m + ((x-t)(y-z))^m \} $$
Prove that $ f_5^2 = f_3 f_7 $
