query: Unable to prove that $n^5-n$ is a multiple of 30.
positive_passages.docid: 3611
positive_passages.text: How to prove $n^5 - n$ is divisible by $30$ without reduction
negative_passages.docid: 126889
negative_passages.text: Proof by induction: inequality $n! > n^3$ for $n > 5$
negative_passages.docid: 114379
negative_passages.text: Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
negative_passages.docid: 82636
negative_passages.text: Maybe is right $\frac{n^2 + 1}{4k + 3} \notin \mathbb{Z}, n, k \in \mathbb{N}^{+}$
negative_passages.docid: 131306
negative_passages.text: Prove that a group of order $2^5 \cdot 7^5$ is not simple
negative_passages.docid: 82913
negative_passages.text: Is this a proof of Fermat's Last Theorem where n = 3?
negative_passages.docid: 44440
negative_passages.text: Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
negative_passages.docid: 19459
negative_passages.text: Find remainder of $F_n$ when divided by $5$
negative_passages.docid: 89184
negative_passages.text: Prove $30|(a^3b-ab^3) $
negative_passages.docid: 41418
negative_passages.text: $2+2 = 5$? error in proof
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: 125618
negative_passages.text: Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
negative_passages.docid: 158799
negative_passages.text: Order of $G$ is 35, are there elements of order 5 and 7 in G?
negative_passages.docid: 23301
negative_passages.text: There does not exist any integer $m$ such that $3n^2+3n+7=m^3$
negative_passages.docid: 55266
negative_passages.text: Prove that $(n+1)^{n-1}<n^n$
negative_passages.docid: 153594
negative_passages.text: When is $1^5 + 2^5 + \ldots + n^5$ a square?
negative_passages.docid: 120290
negative_passages.text: Probability that $7^m+7^n$ is divisible by $5$