MathDB

Real equality in Poly...

Source: CIIM 2021 #2

October 30, 2021

algebra

Problem Statement

Let

r>s

be positive integers. Let

P(x)

and

Q(x)

be distinct polynomials with real coefficients, non-constant(s), such that

P(x)^r-P(x)^s=Q(x)^r-Q(x)^s

for every

x\in \mathbb{R}

. Prove that

(r,s)=(2,1)

.