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Results tagged with diophantine-equations
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user 128426
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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Does $2^x-3p^y=5$ (with $p$ an odd prime) have only finitely many positive integer solutions?
Let $p$ be an odd prime. Does the equation
$$2^x-3p^y=5$$
only have finitely many solutions in positive integers $x$ and $y$?
- 105k