MathDB

Irreducibilty Polynomials

Source: Tuymadaa Senior 2024 P7

July 7, 2024

algebrapolynomial

Problem Statement

Given are two polynomial

f

and

g

of degree

100

with real coefficients. For each positive integer

n

there is an integer

k

such that

\frac{f(k)}{g(k)}=\frac{n+1}{n}.

Prove that

f

and

g

have a common non-constant factor.

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