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Results tagged with diophantine-equations
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user 26522
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 ...
7
votes
Integral points on a particular family of curves
Erdos and Selfridge have proved that the product of two or more consecutive non-zero integers is never a power (Illinois J. Math, vol. 19, no. 2, 1975). This implies in particular that for $n > 1$ a p …
- 13.8k
3
votes
Counting algebraic points of bounded height
This is true. Choose any linear subspace $Z$ (over $K$) of dimension $n- d-1$ and disjoint from $X$, and take $\pi : \mathbb{P}_K^n \setminus Z \to \mathbb{P}_K^d$ the corresponding linear projection. …
- 13.8k