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Abstract Algebra

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Implications of Multiple Congruences

ABSALG-J6LBPY

Let $a,b,c,m,n$ be positive integers. Suppose that $a \equiv b \pmod{n}$ and $b \equiv c \pmod{m}$.

Which of the following must be true?

A

$a \equiv c \pmod{m}$

B

$b^2 \equiv ab+bc-ac \pmod{mn}$

C

$m\equiv n \pmod{abc}$

D

$a+b+c \equiv 0 \pmod{mn}$