Prove that $\varphi(p^k)=p^k-p^{k-1}$ for prime $p$
66061
Why is the formula for calculating euler totient true?
84021
How can we show that $\varphi(a) \neq a +1$ for every $a \in A$?
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
124424
How to show that there is a deduction of $\varphi\leftrightarrow\psi$
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
93898
Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$