MathDB

P3: a^m+b^m=c^m and a^n+b^n=c^n cant hold simultaneously

Source:

March 31, 2013

Problem Statement

Consider three positive real numbers

a,b

and

c

. Show that there cannot exist two distinct positive integers

m

and

n

such that both

a^m+b^m=c^m

and

a^n+b^n=c^n

hold.