Proof of the fact that if a|b and a|c, then a|(b+c)

2.3

Suppose that a|b and a|c.

By the definition of divisibility, a|b means that there is an integer s

such that

b = as.

Similarly, there is an integer t such that

c = at.

Hence, b+c = as+at = a(s+t).

Therefore, a|(b+c).

End of proof.

Previous slide

Next slide

Back to first slide

View graphic version