New posts in Elementary Number Theory

Primes in solutions to Pell-type equations

Prove that $5^n \equiv 8n^2-4n+1 \mod 64$ using induction

Classical number theoretic applications of the $p$-adic numbers

$4q=a^2+27b^2$ elementary proof of uniqueness

If $n>1$, are there $f_1,\dots,f_k\in\mathbb{Z}[x]$ of degree $n$ such that, for any prime $p$, some $f_i$ is irreducible and of degree $n$, mod $p$?

Find all the solutions of $x^2 \equiv 1 \mbox{ mod }365$.

Prove $1^r+2^r+.....\equiv 0\pmod p$ , given that p is odd prime and $0<r<p-1$

$a/p+b/q>1$ with certain conditions

Number Theory : Solve the system of congruence $28x+17y\equiv 18 \pmod{41}$ and $31x+11y\equiv 35\pmod{41}$

An Interesting Number Theory Problem: Solve $2520=(x+y+xy)^2+2xy+2y-3x, x, y \in \mathbb Z$