Thread: Integers

How many pairs of positive integers x and y satisfy the equation x^y=2013²⁰¹³?

Hey chopper07.

(Hint: Try factorizing 2013 first).

chiro's point is that x^y, for x and y integers, will be equal to A if and only if A contains every prime factor of x, to the y power.

For example x^y= 36= 4(9)= 2^2(3^2) only for x= 36, y= 1 or for x= 6, y= 2.