(-1)^{P(1)},(-1)^{P(2)},(-1)^{P(3)},... (I Soros Olympiad 1994-95 R1 11.8)
Source:
August 1, 2021
polynomialalgebraperiodic
Problem Statement
A polynomial with rational coefficients is called integer, if it takes integer values for all integer values of the variable. For an integer polynomial , consider the sequence a) Prove that this sequence is periodic, the period of which is some power of two (i.e. for some integer and for all natural , the -th and ()th members of the sequence are equal).b) Prove that for any periodic sequence consisting of and and with a period of some power of two, there exists a integer, polynomial P for which this sequence is