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Results tagged with diophantine-equations
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user 168119
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 ...
6
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Density of $d$ for which a generalized Pell equation has a solution
Recently Koymans and Pagano have established an asymptotic formula in this setting: $n$ a prime with $n$ congruent to $3$ modulo $4$, within the family of $d$ where $n$ ramifies in $\mathbb{Q}(\sqrt{d …
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