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Tagged with rational-points diophantine-equations
2 questions with no upvoted or accepted answers
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Are the nonnegative rationals diophantine with only two quantifiers?
Definition: A subset $D\subseteq \mathbb{Q}$ is diophantine if it is the projection of the zero set of a polynomial, i.e. there exists a polynomial $f\in\mathbb{Q}[X,Y_1,\dots,Y_n]$ for some $n$ such ...
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Is equation $y^3+x y + x^4 + 4 = 0$ solvable locally (in ${\mathbb Q}_p$ for all $p$)?
When finding out whether an equation in 2 variables has rational solutions (or, equivalently, whether an algebraic curve has any rational points), many authors recommend checking the local solubility ...
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