On solving quadratic congruences

Abstract

The paper proposes a polynomial formula for solution quadratic congruences in ${\mathbb{Z}}_p$. This formula gives the correct answer for quadratic residue and zeroes for quadratic nonresidue. The general form of the formula for $p=3\mathrm{mod}4$, $p=5\mathrm{mod}8$ and for $p=9\mathrm{mod}16$ are suggested.

7 pages