Prove that $n^7$ = n(mod 42)
1895
How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
133819
How to prove that $364 \mid n^{91} - n^7$?
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
11500
Divisibility by 7 rule, and Congruence Arithmetic Laws
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
119152
Proving irreducibility of $x^6-72$
46556
How to prove $3^{\log_4n} = n^{\log_43}$?
32803
Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24)
56574
For any integer $a,b$ let $N_{a,b}$ denote the number of positive integer $x<1000$ satisfying $x= a( mod\;27)$ and $x=b(mod\;37)$. Then
91353
Given $n \in \Bbb Z$, determine $\gcd(3n^2 + 7n + 4, n + 2)$.
46400
how do i prove that $17^n-12^n-24^n+19^n \equiv 0 \pmod{35}$
21476
Modular Exponentiation 3^5^7
149508
Prove $9^n \equiv 9 \pmod{24}\quad \forall n \in \Bbb N^*$
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$