15

Part of 1989 IMO Longlists

Problems(1)

Prove that IMO Longlist 1989 is periodic

Source: IMO Longlist 1989, Problem 15

a_1, a_2, a_3, \ldots

is defined recursively by a_1 \equal{} 1 and a_{2^k\plus{}j} \equal{} \minus{}a_j (j \equal{} 1, 2, \ldots, 2^k). Prove that this sequence is not periodic.

functionalgebrarational functionalgebra unsolved