query: Proving $(11^n -6)$ is divisible by $5$.
positive_passages.docid: 10105
positive_passages.text: Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
negative_passages.docid: 130027
negative_passages.text: Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
negative_passages.docid: 29963
negative_passages.text: $6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
negative_passages.docid: 129238
negative_passages.text: Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
negative_passages.docid: 115733
negative_passages.text: Proving that $\sec\frac{\pi}{11}\sec\frac{2\pi}{11}\sec\frac{3\pi}{11}\sec\frac{4\pi}{11}\sec\frac{5\pi}{11}=32$
negative_passages.docid: 63416
negative_passages.text: Prove $(n^5-n)$ is divisible by 5 by induction.
negative_passages.docid: 152577
negative_passages.text: Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
negative_passages.docid: 101927
negative_passages.text: Induction: Prove that $4^{n+1}+5^{2 n - 1}$ is divisible by 21 for all $n \geq 1$.
negative_passages.docid: 29874
negative_passages.text: Not divisible by $2,3$ or $5$ but divisible by $7$
negative_passages.docid: 145889
negative_passages.text: Prove if $56x = 65y$ then $x + y$ is divisible by $11$
negative_passages.docid: 280
negative_passages.text: Prove by induction that $5^n - 1$ is divisible by $4$.
negative_passages.docid: 85959
negative_passages.text: How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
negative_passages.docid: 100892
negative_passages.text: Proving divisibility of $a^3 - a$ by $6$
negative_passages.docid: 24053
negative_passages.text: How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
negative_passages.docid: 107725
negative_passages.text: Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
negative_passages.docid: 109532
negative_passages.text: Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
negative_passages.docid: 114780
negative_passages.text: $\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof