Has it been proved?

Question

Is sir Fermats last theorem proved for powers which are not integers but are rational numbers etc etc....?

Answer 1

2^(1/2)+2^(1/2)=8^(1/2).
2^(1/3)+2^(1/3)=16^(1/3)
so the result is false with fractional exponents, even if you have integer bases. It may be true for exponents in lowest terms that look like p/q with p>=3.

Answer 2

ermat's Last Theorem states that no nontrivial solutions in integers exist for the equation: x^n + y^n = z^n if n is greater than two.


Andrew Wiles was introduced to Fermat's Last Theorem at the age of ten. He tried to prove the theorem using textbook methods and later studied the work of mathematicians who had tried to prove it. When he began his graduate studies he stopped trying to prove it and began studying elliptic curves under the supervision of John Coates

Answer 3

I think you should reformulate your excellent question

For instance :
Under what cicumstances does the following equation have an integer solution ?
x^p + y^q = z^r

this is equivalent to your excellent question
where p,qand r are rationales.

Answer 4

Maybe?

Answer 5

NO