MathDB

Polynomials evaluated to denominator

Source: 2023 Taiwan TST Round 2 Independent Studey 2-N

April 6, 2023

algebrapolynomialTaiwan

Problem Statement

Find all polynomials

P

with real coefficients satisfying that there exist infinitely many pairs

(m, n)

of coprime positives integer such that

P(\frac{m}{n})=\frac{1}{n}

.
Proposed by usjl