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Given a prime $p\equiv 1\pmod 4$, Fermat's two-squares theorem discovered by Girard states that there exists two integers $A,B$ such that $p=A^2+B^2$. For all primes up to $10^7$ the integers $A$ and $...

I'm trying to use FLINT (Fast Library for Number Theory) to calculate the Legendre Symbol of the following: $$\left(\frac{n! + 1}{p}\right)$$ In my case, $p$ is a positive, odd prime (specifically $...

Looking through some old notes of mine from two years ago I found some crude notes writing what amounted to the statement that for any prime $p\equiv 1\bmod 4$ one could express for any odd integer $p\...

This paper by NC Ankeny mentions that " S. Chowla has proved that there exist infinitely many primes $k$ where the first $c_1\log k$ residues $(\bmod k)$ are all quadratic residues". I recently ...