1. Let a and b be consecutive non-zero whole numbers. Let C be the square of their sum, less their product, i.e. C = (a+b)^2-ab. Let n be a whole number.
Claim 1: C^n = (A+B)^2-AB, for some whole numbers A,B.
Prove it, or find a counter-example.
2. Let a and b be ANY relatively prime whole numbers, and perform the same operation.
Claim 2: C^n = (A+B)^2-AB, for some whole numbers A,B.