MathDB

IMO ShortList 1999, number theory problem 3

Source: IMO ShortList 1999, number theory problem 3

November 13, 2004

modular arithmeticnumber theoryInteger sequenceDivisibilitySequenceIMO ShortlistHi

Problem Statement

Prove that there exists two strictly increasing sequences

(a_{n})

and

(b_{n})

such that

a_{n}(a_{n}+1)

divides

b^{2}_{n}+1

for every natural n.