Number Theory problem mod 2p
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
67332
Sum of two squares modulo p
33735
The square of an integer is congruent to 0 or 1 mod 4
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
74898
$1^n +2^n + \cdots +(p-1)^n \mod p =$?
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
45460
Proof verification of a number theory problem involving sequences.
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
119433
How to find modulo of large numbers like $9801\! \pmod {\!32}$
83542
A natural problem in $\textrm{S}_2^\textrm{P}$?
34617
Number Theory: which primes are a sum of two squares?
22053
Modular Arithmetic - Pirate Problem
102204
Factoring product of two primes from solutions of congruence
14783
A Number Theory problem (GCD)
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$