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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 ...
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
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