Problem

Source: Iran TST1 Day 2 P5

Tags: number theory, sum of digits, Iranian TST



Given kZ prove that there exist infinite pairs of distinct natural numbers such that n+s(2n)=m+s(2m)kn+s(n2)=km+s(m2).(s(n) denotes the sum of digits of n.) Proposed by Mohammadamin Sharifi