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Merton
Merton
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I'm told that Ellenberg and Bruin proved that the Diophantine equation $x^{4} + y^{4} = z^n$ has no primitive solutions in which $xyz\neq 0$ and $n\geq 4$. Does the proof use the same methods that Wiles-Taylor used to prove FLT ? If yes, to what extent is the proof reliant on those methods ? I mean, is the argument heavily based on the techniques that Wiles-Taylor used ?

I'm told that Ellenberg and Bruin proved that the Diophantine equation $x^{4} + y^{4} = z^n$ has no primitive solutions in which $xyz\neq 0$ and $n\geq 4$. Does the proof use the same methods that Wiles used to prove FLT ? If yes, to what extent is the proof reliant on those methods ?

I'm told that Ellenberg and Bruin proved that the Diophantine equation $x^{4} + y^{4} = z^n$ has no primitive solutions in which $xyz\neq 0$ and $n\geq 4$. Does the proof use the same methods that Wiles-Taylor used to prove FLT ? If yes, to what extent is the proof reliant on those methods ? I mean, is the argument heavily based on the techniques that Wiles-Taylor used ?

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Merton
Merton
  • 57
  • 2

On the Diophantine equation $x^{4}+y^{4}= z^n$

I'm told that Ellenberg and Bruin proved that the Diophantine equation $x^{4} + y^{4} = z^n$ has no primitive solutions in which $xyz\neq 0$ and $n\geq 4$. Does the proof use the same methods that Wiles used to prove FLT ? If yes, to what extent is the proof reliant on those methods ?