MathDB

P(n) takes integer values at three consecutive integers

Source: European Girl's MO 2013, Problem 4

April 11, 2013

algebrapolynomialnumber theoryEGMO

Problem Statement

Find all positive integers

a

and

b

for which there are three consecutive integers at which the polynomial

P(n) = \frac{n^5+a}{b}

takes integer values.