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Results tagged with diophantine-equations
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user 116825
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
Existence of solution for a system of quadratic diophantine equations / symmetric quadratic ...
This sketch of a half-answer is based on and is developing the ideas of Max’ answer. He works with $\mathbb Q[I,x]$ with $I^2=-1$ modulo the cyclotomic polynomial $\Phi_p(x)$. Writing $x$ as $z^4$ an …
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