Question

We write $A_{700}(7)=\{[x] \in \mathbb{Z} / 700 \mathbb{Z}:[7][x]=[0]\}$. Show that $A_{700}(7)$ is a field isomorphic to $\mathbb{Z} / 7 \mathbb{Z}$.

   We write $A_{700}(7)=\{[x] \in \mathbb{Z} / 700 \mathbb{Z}:[7][x]=[0]\}$.

Show that $A_{700}(7)$ is a field isomorphic to $\mathbb{Z} / 7 \mathbb{Z}$.

Certain Number-Theoretic Episodes In Algebra

Certain Number-Theoretic Episodes In Algebra

R Sivaramakrishnan 1st Edition

Chapter 1, Problem 12

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It's the set of equivalence classes $[x] \in \mathbb{Z}/700\mathbb{Z}$ such that $[7][x] = [0]$ in $\mathbb{Z}/700\mathbb{Z}$. This means we're looking for all $[x]$ where $7x \equiv 0 \pmod{700}$. Show more…

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We write $A_{700}(7)=\{[x] \in \mathbb{Z} / 700 \mathbb{Z}:[7][x]=[0]\}$. Show that $A_{700}(7)$ is a field isomorphic to $\mathbb{Z} / 7 \mathbb{Z}$.

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