P4

Part of 2022 Latvia Baltic Way TST

Problems(1)

Find a polynomial with n-th power variable

Source: Latvian TST for Baltic Way 2022 P4

p(x)

be a polynomial with real coefficients and

n

be a positive integer. Prove that there exists a non-zero polynomial

q(x)

with real coefficients such that the polynomial

p(x)\cdot q(x)

has non-zero coefficients only by the powers which are multiples of

n

algebrapolynomial