Prove the equation if $b$ is a prime
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
111490
Proof that every number has at least one prime factor
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
54547
Prove this number must be a prime number or 1.
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
127296
prove that a|b and b|a iff a=+-b
110093
Proving that the solution to $f^{\prime}(x) = \frac{1}{x^{2} + (f(x))^{2}}$ is bounded above.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
137920
Proving an equation with invertible matrices
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
136310
Prime number in a polynomial expression
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
29251
Show that the square of any prime number is the Factof of some integer
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$