query: Show that a following equation has no solution in integers: $x^3-x+9=5y^2$
positive_passages.docid: 26461
positive_passages.text: Integer solutions of $x^3-x+9=5y^2$
negative_passages.docid: 77763
negative_passages.text: Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
negative_passages.docid: 35504
negative_passages.text: The Diophantine equation $x^2 + 2 = y^3$
negative_passages.docid: 2027
negative_passages.text: How can I solve the folowing Diophantine equation with two unknowns?
negative_passages.docid: 23835
negative_passages.text: Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.
negative_passages.docid: 32771
negative_passages.text: The equation $X^{n} + Y^{n} = Z^{n}$ , where $ n \geq 3$ is a natural number, has no solutions at all where $X,Y,Z$ are intergers.
negative_passages.docid: 144802
negative_passages.text: Prove no solution to $x^2\equiv3\bmod5$
negative_passages.docid: 41364
negative_passages.text: How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
negative_passages.docid: 28594
negative_passages.text: Number of integer solutions of the following equation
negative_passages.docid: 53503
negative_passages.text: Solving the diophantine equation $y^{2}=x^{3}-2$
negative_passages.docid: 106271
negative_passages.text: Solutions of Diophantine equations in Natural numbers
negative_passages.docid: 99000
negative_passages.text: No polynomial with integer coefficients satisfies the conditions
negative_passages.docid: 55100
negative_passages.text: The positive integer solutions for $2^a+3^b=5^c$
negative_passages.docid: 52960
negative_passages.text: Show that the curve $x^2+y^2-3=0$ has no rational points
negative_passages.docid: 30412
negative_passages.text: How many solutions does the equation $x_1 + x_2 + x_3 = 14$ have, where $x_1$ , $x_2$ , $x_3$ are non-negative integers.
negative_passages.docid: 43470
negative_passages.text: Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.
negative_passages.docid: 41655
negative_passages.text: Simple equation for $x$ but getting no proof.