Can you make new generallization of this theorem for future mathematics
Fermat Last Theorem
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Budi Utomo
5 years, 4 months ago
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Please note that Fermat's last theorem was originated from Pythagoras Theorem, where he (Fermat), must had known a very basic and simple trick which is too elementary to prove, what is the trick?,
"A primitive Pythagoras triplets (in co prime integers), are impossible with two sides of a right angle triangle being as powerful numbers"
Powerful number : is an integer which has all of its prime factors exponent are greater than one
I don't know how to generalize Fermat's Last Theorem, but I can give you a link. This paper is Andrew Wiles' original paper on his proof of Fermat's Last Theorem. It is called "Modular elliptic curves and Fermat's Last Theorem".
We may generalize the exponent to be a real positive algebraic number say (g), the generalization would be as this:
have no solution in distinct positive coprime integers, (X < Y < Z), where (g) is greater than two
This has a specific history that was older than accepted proof of FLT
This link is very useful in this regard: http://hsm.stackexchange.com/questions/3257/sum-of-like-powers-in-real-numbers
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Editt: I mean "A primitive Pythagoras triplets (in co prime integers), are impossible with all sides of a right angle triangle being as powerful numbers", or "A primitive Pythagoras triplets (in co prime integers), are impossible with two sides of a right angle triangle being as powerful numbers of this form (x^n, y^m, z), where (n, m) are positive integers > 1, and (x, y, z) are positive integers"