Find all $[x] \in \mathbb{Z}/30\mathbb{Z}$ such that $[x]^2 = [x] $
I am really not sure how to start on this problem, please help me!
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4How about trying them all in a spreadsheet if you don't have any other idea? Fill Series and Copy Down are your friends. – Ross Millikan Mar 19 '20 at 22:52
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1$x^2\equiv x\mod p$ where $p$ is prime means $x\equiv0 $ or $1\pmod p$. $30=2\times3\times5$ – J. W. Tanner Mar 19 '20 at 22:56
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Hint: $x^2 \equiv x\pmod{30}\iff x^2\equiv x\pmod{p}$ for $p=2,3,5$, and the latter only has $[0]_p$ and $[1]_p$ as solutions.
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