query: Find n and m such that $n²-m²=28$
positive_passages.docid: 157186
positive_passages.text: Finding integers satisfying $m^2 - n^2 = 1111$
negative_passages.docid: 110383
negative_passages.text: How many numbers less than $m$ and relatively prime to $n$, where $m>n$?
negative_passages.docid: 46400
negative_passages.text: how do i prove that $17^n-12^n-24^n+19^n \equiv 0 \pmod{35}$
negative_passages.docid: 3109
negative_passages.text: Prove that $(p+q)^m \leq p^m+q^m$
negative_passages.docid: 35052
negative_passages.text: Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.
negative_passages.docid: 132089
negative_passages.text: How do I prove/disprove that $F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$, where $F_n$ is the $n$th Fibonacci number?
negative_passages.docid: 76527
negative_passages.text: If $x_{m+n} \le x_n+x_m$, then $\lim x_n/n$ exists and is equal to $\inf x_n/n$
negative_passages.docid: 41876
negative_passages.text: Finding an asymptotic for the sum $\sum_{p\leq x}p^m$
negative_passages.docid: 562
negative_passages.text: Formula for calculating $\sum_{n=0}^{m}nr^n$
negative_passages.docid: 125188
negative_passages.text: how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
negative_passages.docid: 14409
negative_passages.text: A problem about function N
negative_passages.docid: 35342
negative_passages.text: Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
negative_passages.docid: 129381
negative_passages.text: Modular equation problem
negative_passages.docid: 51153
negative_passages.text: Number of solutions to $x^2\equiv a\pmod m$
negative_passages.docid: 96647
negative_passages.text: Number theory: Problem involving rational numbers
negative_passages.docid: 44790
negative_passages.text: Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
negative_passages.docid: 130858
negative_passages.text: How can one find $\mu$?