A nasty one?

Question

Show that in the equation
x^(m) = a^(n) - b^(n)
where m>2 & n>2 & m =/= n It is imposible to find the coprime values of "x" , "a" & "b".It is not Fermats last theorem but more generalised form of Fermats last theorem.

Answer 1

Good luck showing this. It is a special case of an open conjecture called Beal's conjecture, worth $100,000 if you can solve the more general situation. See http://mathworld.wolfram.com/BealsConjecture.html for more info. Also look at http://mathworld.wolfram.com/abcConjecture.html for the abc conjecture, often used for problems like this.