query: prove that for every natural n, $5^n - 2^n$, can be divided by 3
positive_passages.docid: 2522
positive_passages.text: Why is $a^n - b^n$ divisible by $a-b$?
negative_passages.docid: 67527
negative_passages.text: Proof by Induction that $3^n ≥ 1+2^n$
negative_passages.docid: 114873
negative_passages.text: Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
negative_passages.docid: 19701
negative_passages.text: Prove $5\mid2^{4n}-1$ by induction
negative_passages.docid: 5257
negative_passages.text: Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
negative_passages.docid: 48051
negative_passages.text: Proof related to natural numbers
negative_passages.docid: 72557
negative_passages.text: Prove that $T(n) = T(n/3) + T2n/3) + 5n$ is $O(n log n)$
negative_passages.docid: 109532
negative_passages.text: Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
negative_passages.docid: 112631
negative_passages.text: Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
negative_passages.docid: 20964
negative_passages.text: Proof that $n^2 < 2^n$
negative_passages.docid: 17965
negative_passages.text: Prove 24 divides $u^3-u$ for all odd natural numbers $u$
negative_passages.docid: 8609
negative_passages.text: Prove by induction that $n!>2^n$
negative_passages.docid: 144447
negative_passages.text: Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
negative_passages.docid: 9302
negative_passages.text: Questions about Divisibility of $2^n$ by $3$
negative_passages.docid: 20477
negative_passages.text: Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
negative_passages.docid: 106847
negative_passages.text: Proof that $n^3+2n$ is divisible by $3$
negative_passages.docid: 55437
negative_passages.text: When does $2^{n}$ divide $3^{n}-1$