query: Solve over the integers the equation $2^n+1=m^2$
positive_passages.docid: 26898
positive_passages.text: Trouble solving two number theoretical problems
negative_passages.docid: 7466
negative_passages.text: How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
negative_passages.docid: 90830
negative_passages.text: Solve the integeral equation (C.S.I.R)
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: 155012
negative_passages.text: Solving quadratic equations in modular arithmetic
negative_passages.docid: 59196
negative_passages.text: Find all real solutions for $x$ in $ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2 . $
negative_passages.docid: 24822
negative_passages.text: How to solve the equation $(z+1)^7 = z^7$ for all $z$?
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 123159
negative_passages.text: Solutions of the diophantine equation $x+y+z=xyz$?
negative_passages.docid: 49794
negative_passages.text: Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
negative_passages.docid: 8504
negative_passages.text: Factoring $x^n + y^n$ over the integers
negative_passages.docid: 48949
negative_passages.text: Solving a Diophantine equation with a large solution
negative_passages.docid: 155363
negative_passages.text: Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
negative_passages.docid: 112390
negative_passages.text: Solutions of $x^2 \equiv 1 \pmod N$
negative_passages.docid: 18203
negative_passages.text: Diophantine equation $a^2+b^2=c^2+d^2$