query: Show that the equation has a natural solution
positive_passages.docid: 134765
positive_passages.text: Is an integer a sum of two rational squares iff it is a sum of two integer squares?
negative_passages.docid: 131141
negative_passages.text: Solutions to $p+1=2n^2$ and $p^2+1=2m^2$ in Natural numbers.
negative_passages.docid: 51029
negative_passages.text: Looking for a hint on the class of a particular equation
negative_passages.docid: 9282
negative_passages.text: Prove using natural deduction $((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$
negative_passages.docid: 22192
negative_passages.text: System of linear equations having a real solution has also a rational solution.
negative_passages.docid: 32071
negative_passages.text: General solution of linear equation = particular + general homogeneous solution
negative_passages.docid: 90261
negative_passages.text: Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
negative_passages.docid: 83542
negative_passages.text: A natural problem in $\textrm{S}_2^\textrm{P}$?
negative_passages.docid: 39921
negative_passages.text: show that f is constant on I
negative_passages.docid: 50994
negative_passages.text: Complex solutions to real equation?
negative_passages.docid: 90970
negative_passages.text: How to prove the line exist?
negative_passages.docid: 91684
negative_passages.text: Prove the following equation(much needed help):
negative_passages.docid: 103501
negative_passages.text: Question about a normal equation proof
negative_passages.docid: 117418
negative_passages.text: Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
negative_passages.docid: 14517
negative_passages.text: Existence of solutions of the equation with a limit.
negative_passages.docid: 71465
negative_passages.text: solution of $y' = \exp \left(-\frac yx\right) + \frac yx$
negative_passages.docid: 151857
negative_passages.text: Explain the equation