Rings & finite fields

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 finite field $\mathbb Z_{7}$, evaluate the polynomial $f(x) = x^{2} + 9x + 2$ at $x = 6$. Give your answer as the representative in the range $0$ to $6$.

2. Warm-up

   Working in the finite field $\mathbb Z_{17}$, evaluate the polynomial $f(x) = x^{2} + 8x + 9$ at $x = 2$. Give your answer as the representative in the range $0$ to $16$.

3. Warm-up

   Working in the finite field $\mathbb Z_{17}$, evaluate the polynomial $f(x) = x^{2} + x + 7$ at $x = 5$. Give your answer as the representative in the range $0$ to $16$.

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