for all prime $p$, how to prove $a = (p!-1)$ is the only integer $a$ that satisfy $p! | (a^p + 1)$?
118039
How prove $p!|(a+1)$ if $p!|a^p+1$
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
119630
For an odd prime $p$, $\;p =1 \pmod 4,\; \;x^2+1 = 0 \pmod p$
38876
$r! \equiv (−1)^k \pmod p$
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
27147
Proving $n! > n^3$ for all $n > a$
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
151153
Prove $\frac{a(a^2+2)}{3}$ is an integer for all integer $a\geqslant 1$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
118212
Is it true that $A^A\simeq P(A)$?
49217
How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$?