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Abstract Algebra

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ABSALG-3LLQHN

Which of the following is FALSE?

You do not need a calculator.

A

$3^4\equiv 1$ mod $10$ and $3^4\equiv 1$ mod $12$.

B

$7^4\equiv 1$ mod $10$ and $7^4\equiv 1$ mod $12$.

C

$3^{807}\equiv 7$ mod $10$.

D

$5^4\equiv 5$ mod $10$ and $5^4\equiv 1$ mod $12$.

E

$3^4\equiv 1$ mod $10$ and $3^4\equiv 9$ mod $12$.