Find the sum of all positive integerscsuch that for some primeaand a positive integerb,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.

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- March 26th 2013, 10:07 AMgeniusgarvilPrime PowerFind 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. - March 26th 2013, 10:23 AMVasanthBalakrishnanRe: Prime Power
this question is from brilliant.org

this is a simple problem involving basic number theory skills

answer is 10 - March 26th 2013, 11:30 PMgeniusgarvilRe: Prime Power
I don't want the answer, i m much more interested in how it came.