Prove $x^x = a + np$ for a prime p
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
129331
Prove that $|x^p - y^p| \le p|x-y|(x^{p-1} + y^{p-1})$ provided that $1 \le p \lt \infty$ and $x, y \ge 0$
148790
Basic question about proofs with the goal $\exists x P(x)$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
78917
Show that for any prime numbers $p,q,r$, one has $p^2+q^2 \ne r^2$.
88328
Proof of $1+x\leq e^x$ for all x?
14448
Elementary proof that $|x|^p$ is convex.
118212
Is it true that $A^A\simeq P(A)$?
42677
Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
114812
Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$