query: number theory division of power for the case $(n^r −1)$ divides $(n^m −1)$ if and only if $r$ divides $m$.
positive_passages.docid: 6012
positive_passages.text: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
negative_passages.docid: 14403
negative_passages.text: If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
negative_passages.docid: 84733
negative_passages.text: Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
negative_passages.docid: 118809
negative_passages.text: If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
negative_passages.docid: 112031
negative_passages.text: Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
negative_passages.docid: 40131
negative_passages.text: If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
negative_passages.docid: 5841
negative_passages.text: Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
negative_passages.docid: 122612
negative_passages.text: An integer is a $n$'th power if that holds true for all moduli.
negative_passages.docid: 50534
negative_passages.text: Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
negative_passages.docid: 136854
negative_passages.text: Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
negative_passages.docid: 152223
negative_passages.text: If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
negative_passages.docid: 82953
negative_passages.text: In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
negative_passages.docid: 72511
negative_passages.text: If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
negative_passages.docid: 50413
negative_passages.text: Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
negative_passages.docid: 117167
negative_passages.text: $3^{n+1}$ divides $2^{3^n}+1$
negative_passages.docid: 141088
negative_passages.text: Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
negative_passages.docid: 104484
negative_passages.text: Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$