- #1

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I encountered a problem I don't know how to solve: In [itex]\mathbb{Z}_{21}[/itex], I want to find numbers

**x**such that [itex]x^2 = x[/itex].

I don't know what to do with that, I just wrote that (since 21 divides [itex]x^2 - x[/itex])

[tex]

21y = x^2 - x

[/tex]

for some integer

**y**, but it didn't seem to help me much.

Could you give me please some advice?

And I have one more (probably trivial, but I can't find it nowhere) question regarding [itex]Z_{n}[/itex]: These fields consist of elements [itex]\{0, 1, ... , n - 1\}[/itex]. But what if I am given something like -7 or [itex]\frac{2}{5}[/itex], how should I represent it in this field?

Thank you.