um of all positive integers $k$ with $1 \le k < n$ and $gcd(k,n)=1$
27069
sum of all positive integers less than $n$ and relatively prime to $n$
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
153763
Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
90806
Find all positive integers $n$ such that $n$ is divisible by all the positive integers less than or equal to $\sqrt{n}$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
66785
Find $\gcd(p^n-1,p^m+1)$.
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
8160
What is $\gcd(0,a)$, where $a$ is a positive integer?
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
70006
$a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then $m|n$?