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Results tagged with diophantine-equations
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user 130364
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 the equation $(xy+1)(xy+x+2)=n^2$ have a positive integer solution?
This is not really an answer, but you can at least observe that $xy+1 \neq xy + x + 2$ if $x$ is positive.
Then consider what kind of common prime factors they could have, since $(xy + 1)(xy + x + 2) …
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