Let m be an integer . Let us say that m is a SPA number if there are positive whole numbers k and j such that

m = (m^k + m^j) / 2.

Find all SPA numbers.

With k>=j, these are some special cases, maybe all cases:

1) m=0

2) m=1

3) k=j           

4) j=2 and k=3 and m=-2 (corrected via Ady)

5) j and k both odd or both even, and m=-1   

Edited on August 4, 2019, 6:32 pm

Posted by Steven Lord on 2019-08-04 11:29:56