## Excel in math and science

### Master concepts by solving fun, challenging problems.

## It's hard to learn from lectures and videos

### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by 4 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

## Comments

Sort by:

TopNewestPlease 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 – Bassam Karzeddin · 11 months, 3 weeks ago

Log in to reply

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 – Bassam Karzeddin · 1 year, 3 months ago

Log in to reply

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". – Ananth Jayadev · 1 year, 4 months ago

Log in to reply

This link is very useful in this regard: http://hsm.stackexchange.com/questions/3257/sum-of-like-powers-in-real-numbers – Bassam Karzeddin · 11 months, 3 weeks ago

Log in to reply

– Bassam Karzeddin · 9 months, 1 week ago

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"Log in to reply