MathDB

Sequences and Number theory

Source: Federal Mathematical Competition of Serbia and Montenegro 2004

May 14, 2018

number theory

Problem Statement

The sequence

(a_n)

is determined by

a_1 = 0

and

(n+1)^3a_{n+1} = 2n^2(2n+1)a_n+2(3n+1)

for

n \geq 1

. Prove that infinitely many terms of the sequence are positive integers.