query: find the smallest $n>1$ such that : $n(n+1)(2n+1)=6m^{2}$
positive_passages.docid: 22840
positive_passages.text: The sum of the first $n$ squares is a square: a system of two Pell-type-equations
negative_passages.docid: 51649
negative_passages.text: prove there is no smallest positive rational number
negative_passages.docid: 108238
negative_passages.text: Find the smallest integer $n$ greater than $1$ such that the last $3$ digits of $n^2$ are the same as the last $3$ digits of $n$.
negative_passages.docid: 50781
negative_passages.text: $(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
negative_passages.docid: 50894
negative_passages.text: Prove that $6$ divides $n(n + 1)(n + 2)$
negative_passages.docid: 20504
negative_passages.text: $\forall m,n \in \Bbb N$ : $\ 56786730\mid mn(m^{60}-n^{60})$
negative_passages.docid: 57644
negative_passages.text: Lower bounds for ${{2n} \choose {n}}$
negative_passages.docid: 142718
negative_passages.text: How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once?
negative_passages.docid: 37650
negative_passages.text: Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
negative_passages.docid: 48655
negative_passages.text: Find all n such that : $3 \mid (n2^{n}+1)$
negative_passages.docid: 48200
negative_passages.text: Simplify $\sum_{i=0}^n (i+1)\binom ni$
negative_passages.docid: 60206
negative_passages.text: Find minimum of $P=\frac{\sqrt{3(2x^2+2x+1)}}{3}+\frac{1}{\sqrt{2x^2+(3-\sqrt{3})x +3}}+\frac{1}{\sqrt{2x^2+(3+\sqrt{3})x +3}}$
negative_passages.docid: 66785
negative_passages.text: Find $\gcd(p^n-1,p^m+1)$.
negative_passages.docid: 12967
negative_passages.text: Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
negative_passages.docid: 64883
negative_passages.text: What is the most efficient algorithm to find the closest prime less than a given number $n$
negative_passages.docid: 24572
negative_passages.text: Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
negative_passages.docid: 6874
negative_passages.text: smallest value of $k$ for which $a_k$ is $0$