MathDB

Writing every integer in form of sum of product of powers

Source: ToT 2003-SA-2

June 19, 2011

inductionnumber theory unsolvednumber theory

Problem Statement

Prove that every positive integer can be represented in the form

3^{u_1} \ldots 2^{v_1} + 3^{u_2} \ldots 2^{v_2} + \ldots + 3^{u_k} \ldots 2^{v_k}

with integers

u_1, u_2, \ldots , u_k, v_1, \ldots, v_k

such that

u_1 > u_2 >\ldots > u_k\ge 0

and

0 \le v_1 < v_2 <\ldots < v_k