s(2n) and s(n^2)
Source: Iran TST1 Day 2 P5
February 23, 2020
number theorysum of digitsIranian TST
Problem Statement
Given prove that there exist infinite pairs of distinct natural numbers such that
\begin{align*}
n+s(2n)=m+s(2m) \\
kn+s(n^2)=km+s(m^2).
\end{align*}
( denotes the sum of digits of .)Proposed by Mohammadamin Sharifi