$a_0+a_1p^1+..+a_kp^{k}=b_0+b_1p^1+..+b_kp^{k}$ imply $\forall\ 0\le i \le k\ a_i=b_i$; $p$ is prime, $\forall\ 0\le i \le k: 0\le a_i,b_i<p$
127468
Prove that there is only one unique base b representation of any natural number.
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
80009
Prove that $| |a|-|b| | \le |a-b|$
151701
Does there exist an $a_0$ such that the sequence $a_{n+1} = 2a_n + 1$ is prime for all $n \ge 0$?
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
118212
Is it true that $A^A\simeq P(A)$?
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
64148
If $p$ and $q$ are distinct primes and $a$ be any integer then $a^{pq} -a^q -a^p +a$ is divisible by $pq$.
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$