New posts in Elementary Number Theory

Find last three digits of $8^{8^8}$

Let $p=40k+9$ be prime. Does $10$ always have even order mod $p$?

Are the numbers $\sqrt{n^2 + q^2}$, $n=0,1,\dots$, linearly dependent over $\mathbb{Q}$?

Determine if the Diophantine equation $x^{2008}-y^{2008}=2^{2009}$ has any solutions.

A puzzle involving $10$-adic numbers

When are eight integers entirely determined by their pairwise sums?

Why do binomial expansions involving surds get closer to integers as they get larger?

Suppose $[a],[b],[c]\in\Bbb Z_n$, and are residue classes which satisfy $[a][b]=[1]$ and $[a][c]=[1]$. Prove $[b]=[c]$.

Find the $26^{th}$ digit of a $50$ digit number divisible by $13$.

What is the probability that the total score after throwing darts is divisible by $3$.