How we can prove that if $p,q$ be prime and $q\mid a^p-1$, then $q\mid a-1$ or $q=2kp+1$?
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
43219
If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$
119282
If $a_1,a_2,\ldots, a_n$ are distinct primes, and $a_1=2$, and $n>1$, then $a_1a_2\cdots a_n+1$ is of the form $4k+3$.
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
98871
How to prove that if a prime divides a Fermat Number then $p=k\cdot 2^{n+2}+1$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
36943
How to prove that $L=${$a^p$: p is prime} isn't regular?
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
71788
Prove existence of multiplicative inverse modulo p when p is prime
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?