1650.31 – Divisibility Theorem (Sum)
Suppose , , and are all counting numbers, and . If two of these numbers are multiples of 7, is the third one also a multiple of 7? Show why or why not.
The answer is yes; here's why:
A multiple of 7 can be written 7, or 7, or whatever, where , , etc. are whole numbers.
So if , and and are multiples of 7, we can say = 7 and = n.
Then , and is also a multiple of 7.
The argument is the same for the other cases, since and .