Constructive proof for $p|x^2+1$
27287
$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
55266
Prove that $(n+1)^{n-1}<n^n$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
57639
Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
77026
Proof with inequalities
57368
Prove that a positive polynomial function can be written as the squares of two polynomial functions
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
49217
How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$?
122741
$x^2$ is congruent to $-1 \bmod p$
109102
Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
93410
How to prove ~ (~P & ~Q) : P ∨ Q by natural deduction
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$