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Results tagged with diophantine-equations
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user 4140
Diophantine equations are polynomial equations $F=0$, or systems of polynomial equations $F_1=\ldots=F_k=0$, where $F,F_1,\ldots,F_k$ are polynomials in either $\mathbb{Z}[X_1,\ldots,X_n]$ of $\mathbb{Q}[X_1,\ldots,X_n]$ of which it is asked to find solutions over $\mathbb{Z}$ or $\mathbb{Q}$. Topics: Pell equations, quadratic forms, elliptic curves, abelian varieties, hyperelliptic curves, Thue equations, normic forms, K3 surfaces ...
10
votes
hard diophantine equation: $x^3 + y^5 = z^7$
Hi,
There is no claim in my cv or elsewhere that me and Sander have solved the equation x^3+y^5+z^7=0. All my cv claims is that we're writing a paper on it! That's not the same thing.
All the best,
…
- 3,142
6
votes
Accepted
Special Case of famous Equation
This kind of problem usually requires a little algebraic number theory. Joe Silverman sketches one possible approach in the comments. Here is another. Let's rewrite as
$$
(2y)^2-5^n=-1.
$$
If $n$ is e …
- 3,142