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Bosnia and Herzegovina TST 1998 Day 2 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 1998

September 20, 2018
Sequencenumber theory

Problem Statement

Sequence of integers {un}n∈N0\{u_n\}_{n \in \mathbb{N}_0} is given as: u0=0u_0=0, u2n=unu_{2n}=u_n, u2n+1=1−unu_{2n+1}=1-u_n for all n∈N0n \in \mathbb{N}_0 a)a) Find u1998u_{1998} b)b) If pp is a positive integer and m=(2p−1)2m=(2^p-1)^2, find umu_m
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