IMO 1989 LL CZS15

A sequence a1, a2, a3, . . . is defined recursively by a1 = 1 and

imolonglistmathematicsolympiad

IMO 1989 LL CZS15

Origin: CZS

Problem

A sequence a1, a2, a3, . . . is defined recursively by a1 = 1 and a2k+j = −aj (j = 1, 2, . . . , 2k). Prove that this sequence is not periodic.