Modular arithmetic & congruences

What the problems look like

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

1. Warm-up

   Working in the ring $\mathbb{Z}/8\mathbb{Z}$, compute the least nonnegative residue of $20\cdot19+5$ modulo $8$.

2. Warm-up

   Working in the ring $\mathbb{Z}/10\mathbb{Z}$, compute the least nonnegative residue of $17\cdot20+3$ modulo $10$.

3. Warm-up

   Working in the ring $\mathbb{Z}/5\mathbb{Z}$, compute the least nonnegative residue of $17\cdot10+18$ modulo $5$.

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