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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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Diophantine system

Consider a sequence of integers $n_i,\ i=1,\ldots, N$ and $\nu_k=\sum_{i=k}^N n_i$. Consider a sequence $\Delta_i,\ i=0,\ldots, N+1$ with $\Delta_i\in \{0,1\}$ and $\Delta_0=\Delta_{N+1}=0$. For $i=0, …
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