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Results tagged with diophantine-equations
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user 119063
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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When is the following fraction an integer $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$ where $... [closed]
I'm trying to evaluate the following fraction $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$, but I'm getting stuck using gcd arguments or divisibility arguments. This is part of an ongoing research I'm h …
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