Questions on more advanced topics of number theory, such as quadratic residues, primitive roots, prime numbers, non-linear Diophantine equations, etc. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.

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12
votes
1answer
96 views
+100

Are there infinitely many primes $n$ such that $\mathbb{Z}_n^*$ is generated by $\{ -1,2 \}$?

Let $n$ a prime, and let $\mathbb{Z}_n$ denote the integers modulo $n$. Let $\mathbb{Z}^*_n$ denote the multiplicative group of $\mathbb{Z}_n$ Are there infinitely many $n$ such that $\mathbb{Z}^*_n$ ...
5
votes
2answers
173 views
+50

Find last 5 significant digits of 2017!

Since there are less powers of $5$ than of $2$ and since $10 = 2 \cdot 5$, I counted the number of zeros in $2017!$: $\left \lfloor{ \frac{2017}{5^1}}\right \rfloor + \left \lfloor{ \frac{2017}{5^2}}\...