Hw12 Problem 5

Return to Homework 12, Glossary, Theorems

Problem: Find all solutions of $x^{2} +x -6 = 0$ in the ring (a) $\mathbb{Z}_{14}$ and (b) $\mathbb{Z}_{16}$.


Solution:

(a) Plugging in elements of $\mathbb{Z}_{14}$ into the polynomial yields $x=2,4,9,11$.

(b) Plugging in elements of $\mathbb{Z}_{16}$ into the polynomial yields $x=2,13$.

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