MathDB

IMO ShortList 1998, number theory problem 8

Source: IMO ShortList 1998, number theory problem 8

October 22, 2004

number theoryInteger sequenceAdditive combinatoricsAdditive Number TheoryIMO Shortlist

Problem Statement

Let

a_{0},a_{1},a_{2},\ldots

be an increasing sequence of nonnegative integers such that every nonnegative integer can be expressed uniquely in the form

a_{i}+2a_{j}+4a_{k}

, where

i,j

and

k

are not necessarily distinct. Determine

a_{1998}