Let $a$ and $ b$ be positive integers (of one or more digits) such that $ b$ is divisible by $a$, and if we write $a$ and $ b$, one after the other in this order, we get the number $(a + b)^2$. Prove that $\frac{b}{a}= 6$.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 3.6
Tags: number theory, Digits, divisible