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Results tagged with diophantine-equations
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user 477267
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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Why is Hilbert’s 11th problem still partially resolved?
Hilbert’s 11th problem which demands that we ‘classify quadratic forms over algebraic number fields’ has been of interest to me and I would like to know what makes it partially resolved currently. Or …
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Diophantine equation $2(x - 1/x) = y - 1/y$
When the Diophantine problem above is expressed as:
xy^2 + (2-2x^2)y - x = 0 (1)
and solved with respect to “y”, you would arrive at x=1 or x=-1 and consequently giving y=1 or y=-1 respectively when s …
- 57