query: Given $a_2 = 2$ and $a_{mn}=a_m a_n$ for $m$, $n$ coprime, show $a_n=n$ for all natural numbers
positive_passages.docid: 137750
positive_passages.text: Let $(a_n)$ be a strictly increasing sequence of positive integers such that: $a_2 = 2$, $a_{mn} = a_m a_n$ for $m, n$ relatively prime.
negative_passages.docid: 23684
negative_passages.text: Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
negative_passages.docid: 96329
negative_passages.text: Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
negative_passages.docid: 48839
negative_passages.text: Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
negative_passages.docid: 8884
negative_passages.text: Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
negative_passages.docid: 12210
negative_passages.text: Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
negative_passages.docid: 17601
negative_passages.text: How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
negative_passages.docid: 105671
negative_passages.text: Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
negative_passages.docid: 120976
negative_passages.text: Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
negative_passages.docid: 134365
negative_passages.text: When is this true: If $m^2$ is a multiple of N then m is a multiple of N
negative_passages.docid: 124685
negative_passages.text: How to show $(mn)!$ is divisible by $(m!)^n$?
negative_passages.docid: 66748
negative_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
negative_passages.docid: 6012
negative_passages.text: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
negative_passages.docid: 21781
negative_passages.text: Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
negative_passages.docid: 98946
negative_passages.text: Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
negative_passages.docid: 74631
negative_passages.text: For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
negative_passages.docid: 25004
negative_passages.text: Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically