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Results tagged with diophantine-equations
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user 501020
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 ...
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On quadratic Diophantine equations with n variables
Consider the following problem. Given a quadratic equation
$$ \sum_{i,j=1}^n a_{i,j} x_ix_j + \sum_{k=1}^n d_{k} x_k + e = 0, \qquad a_{i,j},d_k,e\in\mathbb{Z}$$
if it exists, find (at least) a intege …
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Number of solution to homogeneous linear Diophantine equations
Let $T,M\in\mathbb{N}$ be fixed. Consider a linear Diophantine equation of the form
$a_1 x_1 + a_2 x_2 + … + a_n x_n = 0 $
with $a_i \in [-T,T] \subset \mathbb{Z}$. Is there an asymptotic formula to e …
- 11