MathDB

\sqrt{xy} is an integer with the digits of n in reverse order, 2n = x + y

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 3.3

September 21, 2021

number theoryDigits

Problem Statement

Let

x, y

be two positive integers, with

x> y

, such that

2n = x + y

, where n is a number two-digit integer. If

\sqrt{xy}

is an integer with the digits of

n

but in reverse order, determine the value of

x - y