query: Divisibility result by induction: $64 \mid 3^{2n + 2} - 8n - 9$
positive_passages.docid: 153281
positive_passages.text: Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers
negative_passages.docid: 48333
negative_passages.text: Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
negative_passages.docid: 108382
negative_passages.text: Prove $x^n-1$ is divisible by $x-1$ by induction
negative_passages.docid: 130615
negative_passages.text: divisibility of binomial coefficients by primes
negative_passages.docid: 10191
negative_passages.text: Binomial theorem: divisibility by $n^2$
negative_passages.docid: 122711
negative_passages.text: Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.
negative_passages.docid: 82358
negative_passages.text: How to prove that $4^m + 5^m$ is divisible by 9 when m is an odd number
negative_passages.docid: 44906
negative_passages.text: Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
negative_passages.docid: 100558
negative_passages.text: Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
negative_passages.docid: 122386
negative_passages.text: How do I prove that $3$ divides $14^{2n}-1$ by induction?
negative_passages.docid: 113119
negative_passages.text: Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
negative_passages.docid: 97805
negative_passages.text: $n+1$ is a divisor of $\binom{2n} {n}$
negative_passages.docid: 33757
negative_passages.text: For what natural numbers is $n^3 < 2^n$? Prove by induction
negative_passages.docid: 962
negative_passages.text: divisibility problem using induction
negative_passages.docid: 25054
negative_passages.text: Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
negative_passages.docid: 62177
negative_passages.text: Prove that: $2^n < n!$ Using Induction
negative_passages.docid: 9302
negative_passages.text: Questions about Divisibility of $2^n$ by $3$