MathDB

exponential equation (x^x = y^y)

Source:

November 15, 2009

number theoryrelatively prime

Problem Statement

Let x \equal{} \sqrt[3]{\frac{4}{25}}\,. There is a unique value of

y

such that

0 < y < x

and x^x \equal{} y^y. What is the value of

y

? Express your answer in the form

\sqrt[c]{\frac{a}{b}}\,

, where

a

and

b

are relatively prime positive integers and

c

is a prime number.