Find $a$ in $a^2 \equiv 1 \pmod b$ given $b$ where $a < b-1$
42032
Find all solutions to $x^2\equiv 1\pmod {91},\ 91 = 7\cdot 13$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
134450
Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
18053
Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
18093
Find $x$ such that $\sum_{k=1}^{2014} k^k \equiv x \pmod {10}$
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
144017
How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$
36043
If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
145966
Find $P(A\ xor\ B\ |\ A\ \cup\ B)$
105873
Construct an algorithm to find the multiple of A such that A%B is maximized
148458
$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
11989
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
110752
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$