MathDB

Commutative Exponentiation

Source: AIME 2010I Problem 3

March 17, 2010

number theoryrelatively prime

Problem Statement

Suppose that y \equal{} \frac34x and x^y \equal{} y^x. The quantity x \plus{} y can be expressed as a rational number

\frac{r}{s}

, where

r

and

s

are relatively prime positive integers. Find r \plus{} s.