query: Prove that there are no integer solutions to the equation below
positive_passages.docid: 147485
positive_passages.text: A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.
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: 95494
negative_passages.text: Number of solutions of an arithmetic function's equation
negative_passages.docid: 77024
negative_passages.text: Find the number of solutions of $x^2=x\mod m$ for any integer $m$
negative_passages.docid: 48949
negative_passages.text: Solving a Diophantine equation with a large solution
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 41655
negative_passages.text: Simple equation for $x$ but getting no proof.
negative_passages.docid: 63194
negative_passages.text: Find all integer solutions to $x^2-2y^2=1$
negative_passages.docid: 24837
negative_passages.text: $x^2+1=0$ uncountable many solutions
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: 13120
negative_passages.text: Find all integer solutions to $x^2+y^2+z^2=2xyz$
negative_passages.docid: 155743
negative_passages.text: Why does the equation $x^2\equiv2 \pmod 5$ have no solutions?
negative_passages.docid: 72023
negative_passages.text: Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
negative_passages.docid: 101169
negative_passages.text: Prove that $x^2 = - 1$ has no solution in $\mathbb{Z}$
negative_passages.docid: 106271
negative_passages.text: Solutions of Diophantine equations in Natural numbers
negative_passages.docid: 85383
negative_passages.text: No. Of real roots of an equation
negative_passages.docid: 147325
negative_passages.text: Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either