5

Part of 2023 Romanian Master of Mathematics

Problems(1)

2023 RMM, Problem 5

Source: 2023 RMM, Problem 5

P,Q,R,S

be non constant polynomials with real coefficients, such that

P(Q(x))=R(S(x))

and the degree of

P

is multiple of the degree of

R.

Prove that there exists a polynomial

T

with real coefficients such that

\displaystyle P(x)=R(T(x))

PolynomialsRMM 2023number theoryalgebra