query: How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
positive_passages.docid: 66016
positive_passages.text: Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
negative_passages.docid: 12729
negative_passages.text: Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
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: 21100
negative_passages.text: Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
negative_passages.docid: 33757
negative_passages.text: For what natural numbers is $n^3 < 2^n$? Prove by induction
negative_passages.docid: 39716
negative_passages.text: Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
negative_passages.docid: 22592
negative_passages.text: $1\cdot 3 + 2\cdot 4 + 3\cdot 5 + \cdots + n(n+2) = n(n+1)(2n+7)/6$ by mathematical induction
negative_passages.docid: 92046
negative_passages.text: Proving $\sum\limits_{i=0}^n  i 2^{i-1} = (n+1) 2^n - 1$ by induction
negative_passages.docid: 280
negative_passages.text: Prove by induction that $5^n - 1$ is divisible by $4$.
negative_passages.docid: 38995
negative_passages.text: Induction proof that $\sum_{j=n}^{2n-1} (2j + 1) = 3n^2$ - what happened?
negative_passages.docid: 54055
negative_passages.text: Proof $\prod_{i = 1}^n \frac{n + i}{2i-3} = 2^n(1-2n)$ using inducction
negative_passages.docid: 105854
negative_passages.text: Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
negative_passages.docid: 52644
negative_passages.text: Prove $2^k+1$ divisible by 3 for odd K
negative_passages.docid: 11867
negative_passages.text: Prove by induction that $n < 2^n$ for all $n \ge 1$
negative_passages.docid: 17194
negative_passages.text: $6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$
negative_passages.docid: 91921
negative_passages.text: Divisibility of $n\cdot2^n+1$ by 3.
negative_passages.docid: 6561
negative_passages.text: Prove that the expression $5^{2n+1} \cdot 2^{n+2} + 3^{n+2} \cdot 2^{2n+1}$ is divisible by 19.