Problem #PRU-35257

Problems Algebra and arithmetic Polynomials Algebraic identities for polynomials Factoring polynomials
 13–14  3.0

Problem

Prove that, if \(b=a-1\), then \[(a+b)(a^2 +b^2)(a^4 +b^4)\dotsb(a^{32} +b^{32})=a^{64} -b^{64}.\]