query: How to show $15 \mid 2^{4n}-1$ by induction
positive_passages.docid: 19701
positive_passages.text: Prove $5\mid2^{4n}-1$ by induction
negative_passages.docid: 53162
negative_passages.text: $13\mid4^{2n+1}+3^{n+2}$
negative_passages.docid: 79657
negative_passages.text: Prove by induction $\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$ for $n\ge1$
negative_passages.docid: 45037
negative_passages.text: Show $(2^m-1,2^n+1)=1$ if $m$ is odd
negative_passages.docid: 39175
negative_passages.text: Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
negative_passages.docid: 90789
negative_passages.text: Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
negative_passages.docid: 152577
negative_passages.text: Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
negative_passages.docid: 125297
negative_passages.text: Induction to prove $2n + 3 < 2^n$
negative_passages.docid: 134000
negative_passages.text: Proof by Strong Induction: $n = 2^a b,\, b\,$ odd, every natural a product of an odd and a power of 2
negative_passages.docid: 101899
negative_passages.text: Proof By Induction of a Sum
negative_passages.docid: 44897
negative_passages.text: Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
negative_passages.docid: 45914
negative_passages.text: Proving that $n!≤((n+1)/2)^n$ by induction
negative_passages.docid: 78416
negative_passages.text: Show that $7$ divides $a^{15}-a^3$ for any integer $a$
negative_passages.docid: 119118
negative_passages.text: Prove $n\mid \phi(2^n-1)$
negative_passages.docid: 70625
negative_passages.text: Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$
negative_passages.docid: 14435
negative_passages.text: Show by induction: $(1+\frac{1}{n})^{n}<n$
negative_passages.docid: 125618
negative_passages.text: Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction