MathDB
b/a= 6 if b is divisible by a, overline{ab}= (a + b)^2

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 3.6

September 25, 2021
number theoryDigitsdivisible

Problem Statement

Let aa and b b be positive integers (of one or more digits) such that b b is divisible by aa, and if we write aa and b b, one after the other in this order, we get the number (a+b)2(a + b)^2. Prove that ba=6\frac{b}{a}= 6.
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