MathDB

RMM2011, P 2, Day 1 - Find polynomials with integer values

Source:

February 25, 2011

algebrapolynomialmodular arithmeticfunctionnumber theorygreatest common divisorsystem of equations

Problem Statement

Determine all positive integers

n

for which there exists a polynomial

f(x)

with real coefficients, with the following properties:
(1) for each integer

k

, the number

f(k)

is an integer if and only if

k

is not divisible by

n

; (2) the degree of

f

is less than

n

.
(Hungary) Géza Kós