MathDB

Show that $P(n)\in\mathbb{Z}, \forall n\in\mathbb{N}$

Source: Moldova TST 1997

August 8, 2023

algebrapolynomial

Problem Statement

Let

P(X)

be a polynomial with real coefficients such that

\{P(n)\}\leq\frac{1}{n}, \forall n\in\mathbb{N}

, where

\{a\}

is the fractional part of the number

a

. Show that

P(n)\in\mathbb{Z}, \forall n\in\mathbb{N}