MathDB

constant sequence

Source: Austria 1985

July 7, 2009

number theory unsolvednumber theory

Problem Statement

A sequence

(a_n)

of positive integers satisfies: a_n\equal{}\sqrt{\frac{a_{n\minus{}1}^2\plus{}a_{n\plus{}1}^2}{2}} for all

n \ge 1

. Prove that this sequence is constant.