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number of the form $2^p3^q$

Source: 6-th Taiwanese Mathematical Olympiad 1997

January 18, 2007

number theory unsolvednumber theory

Problem Statement

Show that every number of the form

2^{p}3^{q}

, where

p,q

are nonnegative integers, divides some number of the form

a_{2k}10^{2k}+a_{2k-2}10^{2k-2}+...+a_{2}10^{2}+a_{0}

, where

a_{2i}\in\{1,2,...,9\}