MathDB

3^m*2^n representation

Source: BdMO 2023 Secondary National P7

February 12, 2023

number theorystrong induction

Problem Statement

Prove that every positive integer can be represented in the form

3^{m_1}\cdot 2^{n_1}+3^{m_2}\cdot 2^{n_2} + \dots + 3^{m_k}\cdot 2^{n_k}

where

m_1 > m_2 > \dots > m_k \geq 0

and

0 \leq n_1 < n_2 < \dots < n_k

are integers.