Prove that $1^2\cdot3^2\cdot5^2\cdots(p-2)^2 \equiv (-1)^{(p+1)/2} \pmod p$
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
66707
How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
76267
Prove that: $x_1\cdot x_2\cdots x_n>y_1\cdot y_2\cdots y_m$.
78356
How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$
9435
Prove that $1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}$ for $n \in \mathbb{N}$.
134450
Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
11989
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
8602
Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$