5

Part of 1985 Federal Competition For Advanced Students, P2

Problems(1)

constant sequence

Source: Austria 1985

(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.

number theory unsolvednumber theory