I am not sure if I am approaching the problem below in the right way. Is there any chance that someone can check it for me,please?
Show that the equation
I assumed by contradiction that is an integer solution to our problem and it has the smallest value of of any such solution.
We can also note that is in fact a Pythagoran triple as .
for some co-prime integers . Let be even and be odd, but that also imlpies that either or is divisible by . Hence contradict the fact that they are integer.
February 12th 2013, 08:27 PM
Re: Fermat Last Theorem
If I were grading your answer, I wouldn't accept it. What do you mean by divides an integer?
Suppose x, y and z satisfy the equation. As you point out, we can assume gcd(x,y,z)=1. Clearly 3 divides x, so write , and the equation becomes . So 3 divides . Since gcd(x,y,z)=1, 3 does not divide both and . So 3 can divide neither. But then both and must be 1 mod 3, and so is 2 mod 3, and not 0. Contradiction.