How many pairs of positive integers x and y satisfy the equation x^{y}=2013^{2013}?

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- Feb 7th 2013, 05:10 PMchopper07Integers
How many pairs of positive integers x and y satisfy the equation x

^{y}=2013^{2013}? - Feb 8th 2013, 12:39 AMchiroRe: Integers
Hey chopper07.

(Hint: Try factorizing 2013 first). - Feb 8th 2013, 06:28 AMHallsofIvyRe: Integers
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.