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If A and B are multiples of C, then A + B is also a multiple of C:

If A is a multiple of C then A = mC for some integer m

If B is a multiple of C, then B = nC for some integer n

→ A + B = mC + nC

= (m + n)C

= kC where k = m + n and is an integer

→ A + B is a multiple of C

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