Determine all positive integers $n$ such that $n$ equals the square of the sum of the digits of $n$.
Problem
Source: Singapore Senior Math Olympiad 2012 2nd Round p2 SMO
Tags: sum of digits, number theory, square
Source: Singapore Senior Math Olympiad 2012 2nd Round p2 SMO
Tags: sum of digits, number theory, square
Determine all positive integers $n$ such that $n$ equals the square of the sum of the digits of $n$.