MathDB

periodic with period $2^k$

Source: 8th IMAR,problem 1

January 1, 2012

algebrapolynomialalgebra proposed

Problem Statement

Show that a sequence

(a_n)

+1

and

-1

is periodic with period a power of

2

if and only if

a_n=(-1)^{P(n)}

, where

P

is an integer-valued polynomial with rational coefficients.