Show that, for every integer $a$ such that $\gcd(a,100)=1$, we have $a^{20}≡1\pmod{100}$.
98380
$x^{20}=1$ for all $x\in U(100)$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
36611
Algorithms for solving the discrete logarithm $a^x \equiv b\pmod{n}$ when $\gcd(a,n) \neq 1$
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
61825
Congruence class $[a]$ modulo $m$, $\gcd(x, m) = \gcd(a, m)$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
1713
number theory $\gcd(a,bc)=\gcd(a,c)$