Question

Prove that for all integers "a" and "b" there is an integer "c" such that a|c and b|c

Answer 1

Does 1 counts?

Answer 2

what is that symbol denoting?

Answer 3

division!!! :-)

Answer 4

\[2 \nmid 1\], so c does not work. Try \(c=a\cdot b\)

Answer 5

That should read \(c=1\) does not work.

But if we let \(c=a\cdot b\), we basically have the proof by definition of divisibility right here. \(a|c\) since there exists some integer \(k\) (in this case \(k=b\)) such that \(c=a\cdot k\). It follows from a symmetrical argument that \(b|c\).

Answer 6

No idea how to prove it. Using strong inductions?