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Results tagged with diophantine-equations
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user 39521
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 ...
3
votes
Is there an algorithm to solve quadratic Diophantine equations?
We first run the algorithm to determine whether any solutions exist, by dovetailing an enumeration of integer $n$-tuples together with an exhaustive search of solutions modulo prime powers, halting if …
- 12.4k
24
votes
Accepted
Rational inscribed realization of the regular dodecahedron
An example
Yes, here is a list of rational coordinates lying on the unit sphere, the convex hull of which is combinatorially equivalent to a regular dodecahedron. This polyhedron is invariant under r …
- 12.4k