Find all nonzero integer solutions of this system of equations:

A^A+B= B¹² and, B^A+B = A³

Prove that there are no others.

(In reply to Analytical Solution by Steve Herman)

(1,-1) appears to be a solution also.

1^{(1 + -1)} = -1¹²
1⁽⁰⁾ = 1 ... & ... -1¹²  = 1

-1^{(1 + -1)} = 1³
-1⁽⁰⁾ = 1 ... & ... 1³  = 1

Posted by Dej Mar on 2015-03-29 22:50:51