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Abstract Algebra

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Moderate

Product of Two Residue Classes mod m

ABSALG-GJFG6E

Which of the following statements is TRUE?

Select ALL that apply.

A

If $ab\equiv 0$ mod $5$ then either $a\equiv0$ mod $5$ or $b\equiv 0$ mod $5$

B

If $ab\equiv 0$ mod $15$ then either $a\equiv0$ mod $15$ or $b\equiv 0$ mod $15$

C

The congruence $5x\equiv 1$ mod $18$ has more than one solution mod $18$

D

The congruence $3x\equiv 6$ mod $18$ has more than one solution mod $18$

E

The congruence $3x\equiv 6$ mod $18$ has one solution mod $18$