The DioFermat Equation

Number Theory Level 2

$\large {x^3+y^3=z^3}$ If $x, y\, \&\, z$ are non-zero integers, then find the total number of ordered triples ${(x,y,z)}$ for which the equation above is true.

The answer is 0.

2 solutions

Mehul Arora
Sep 8, 2015

According to Fermat's last theorem, $a^n + b^n = c^n (abc \neq 0)$ only if $n \leq 2$ Thus. No solution.

You should mention the condition $abc\neq0$ .

MD Omur Faruque - 5 years, 9 months ago

He did say a!=0,b!=0and c!=0 hence abc !=0.it is understood.

Rajat Pandey - 5 years, 9 months ago

That was after my comment.

MD Omur Faruque - 5 years, 9 months ago

Md Mehedi Hasan
Nov 9, 2017

It's solvable using Fermat's last theorem. From it we get, for $x,y,z\neq 0$ and $n\ge 2$

$\large x^n+y^n=z^n$

have no any solution for $(x,y,z)$

The DioFermat Equation

The answer is 0.

2 solutions

0 pending reports