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Given the ring $ \mathbb{Z}/n\mathbb{Z} $ is always true that $ \mathbb{Z}/n\mathbb{Z}=[\text{zero divisors}]\cup[\text{units}] $

How can evaluate the zero divisors and units ?

I believe that $ a x=0 \pmod n $ for zero divisor

and $ ax=1 \pmod n $ for units

I know how to solve a congruence but what is $a$ ?? thanks.

What are the generators of the group $ \mathbb{Z}/n\mathbb{Z} $ under the addition '+' and product '$\times$'?

3 Answers 3