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Results tagged with diophantine-equations
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user 110554
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 ...
5
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answer
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Undecidability of Diophantine equations with disjoint variables?
Consider a special case of the Hilbert's 10th problem:
$f(\vec{x})=g(\vec{y})$, where $\vec{x}$ and $\vec{y}$ are disjoint ( i.e, the LHS and RHS do not have any common variables), moreover, $f$ and …
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