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Results tagged with nt.number-theory
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user 126005
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
9
votes
1
answer
488
views
Enquiry on a Diophantine problem
Let $x,y, z$ be relatively prime integers with $xyz \neq 0$. Suppose that
$$x^{m/n} + y^{m/n} = z^{m/n}$$
where $m,n$ are relatively prime integers with $mn \neq 0$.
Does it necessarily follow tha …
- 141
5
votes
2
answers
417
views
On the Diophantine equation $x^{4}+y^{4}=z^p$
Do there exist integers $x,y,z$ with $xyz\neq 0$, such that
$$x^4 + y^4 = z^p$$
where $p\geq 5$ is some prime ?
If yes, are there infinitely many of them ? And if there exists infinitely many of th …
- 141