Modular arithmetic

What the problems look like

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

1. Warm-up

   Reduce $40$ and $79$ mod $15$, then compute $(40 \cdot 79 + 8) \bmod 15$. Give (i) $40 \bmod 15$; (ii) $79 \bmod 15$; (iii) the final value $(40 \cdot 79 + 8) \bmod 15$.

2. Warm-up

   Reduce $70$ and $18$ mod $4$, then compute $(70 \cdot 18 + 38) \bmod 4$. Give (i) $70 \bmod 4$; (ii) $18 \bmod 4$; (iii) the final value $(70 \cdot 18 + 38) \bmod 4$.

3. Warm-up

   Reduce $70$ and $43$ mod $11$, then compute $(70 \cdot 43 + 35) \bmod 11$. Give (i) $70 \bmod 11$; (ii) $43 \bmod 11$; (iii) the final value $(70 \cdot 43 + 35) \bmod 11$.

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