IMO 2011 Shortlist N4
For each positive integer k, let t(k) be the largest odd divisor of k. Determine all positive integers a for which there...
Category: Number Theory
Problem
For each positive integer k, let t(k) be the largest odd divisor of k. Determine all positive integers a for which there exists a positive integer n such that all the differences t(n + a) − t(n), t(n + a + 1) − t(n + 1), ..., t(n + 2a − 1) − t(n + a − 1) are divisible by 4.