query: Prove: $\text{ord}(a^m) = \frac{\text{lcm}(m,n)}{m}$
positive_passages.docid: 83654
positive_passages.text: Order of an element in a finite cyclic group
negative_passages.docid: 128710
negative_passages.text: Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
negative_passages.docid: 52642
negative_passages.text: Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
negative_passages.docid: 16548
negative_passages.text: Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
negative_passages.docid: 11989
negative_passages.text: $ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
negative_passages.docid: 25648
negative_passages.text: Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$
negative_passages.docid: 53426
negative_passages.text: Proof of a formula involving Euler's totient function: $\varphi (mn) = \varphi (m) \varphi (n) \cdot \frac{d}{\varphi (d)}$
negative_passages.docid: 48452
negative_passages.text: Proof that $\gcd$ divides $\operatorname{lcm}$
negative_passages.docid: 21288
negative_passages.text: For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
negative_passages.docid: 100361
negative_passages.text: Show that ord$_{p}2 = 2^{n + 1}$.
negative_passages.docid: 23590
negative_passages.text: Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
negative_passages.docid: 152039
negative_passages.text: Prove that $a^{2^n}=1 \mod 2^{n+2}$
negative_passages.docid: 2626
negative_passages.text: Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
negative_passages.docid: 28749
negative_passages.text: Proving that any common multiple of two numbers is a multiple of their least common multiple
negative_passages.docid: 49109
negative_passages.text: Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
negative_passages.docid: 72747
negative_passages.text: Proving gcd($a,b$)lcm($a,b$) = $|ab|$
negative_passages.docid: 14693
negative_passages.text: $d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]