Quadratic residues

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Find the least non-negative residue of $6^{2}$ modulo the prime $37$ — that is, the quadratic residue that $6$ produces modulo $37$.

2. Warm-up

   Find the least non-negative residue of $17^{2}$ modulo the prime $23$ — that is, the quadratic residue that $17$ produces modulo $23$.

3. Warm-up

   Find the least non-negative residue of $4^{2}$ modulo the prime $41$ — that is, the quadratic residue that $4$ produces modulo $41$.

Problems shown under their original terms: Generated (template, solver-computed).