# Prime Power

• Mar 26th 2013, 09:07 AM
geniusgarvil
Prime Power
Find the sum of all positive integers c such that for some prime a and a positive integer b,
a^b+b^a=c^a.
tried taking the second term to the RHS and checked factorizing it. Than i got that a^b is equal to c-b or the remaining term.
• Mar 26th 2013, 09:23 AM
VasanthBalakrishnan
Re: Prime Power
this question is from brilliant.org

this is a simple problem involving basic number theory skills