query: Proof of 42 | $n^7-n$
positive_passages.docid: 24053
positive_passages.text: How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
negative_passages.docid: 21612
negative_passages.text: How to prove this form of $n$?
negative_passages.docid: 146867
negative_passages.text: Combinatorial Proof Of A Number Theory Theorem--Confusion
negative_passages.docid: 114867
negative_passages.text: Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
negative_passages.docid: 16660
negative_passages.text: Prove that any positive number has an $n$th root
negative_passages.docid: 41641
negative_passages.text: $(n-7)(n+7)=$ some perfect square
negative_passages.docid: 133017
negative_passages.text: Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
negative_passages.docid: 22073
negative_passages.text: Prove by induction that $n^2<n!$
negative_passages.docid: 27449
negative_passages.text: Product of Divisors of some $n$ proof
negative_passages.docid: 89175
negative_passages.text: Proof of $(a+b)^{n+1}$
negative_passages.docid: 23684
negative_passages.text: Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
negative_passages.docid: 24403
negative_passages.text: Prove that $ n < 2^{n}$ for all natural numbers $n$.
negative_passages.docid: 119152
negative_passages.text: Proving irreducibility of $x^6-72$
negative_passages.docid: 149216
negative_passages.text: Give a combinatorial proof to show the following for all integers $n \geq 2$.
negative_passages.docid: 99428
negative_passages.text: Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.
negative_passages.docid: 115016
negative_passages.text: Prove that the number of $\alpha\in\mathbb{F}_{27}$ such that $|A_\alpha|=26 $ equals 12.
negative_passages.docid: 81136
negative_passages.text: Prove by induction that... $1+3+5+7+...+(2n+1)=(n+1)^2$ for every $n \in \mathbb N$