Question

Show that if a and b are integers, that are not both zero, and c is a nonzero integer, then (ca , cb) : lclb, b\.

Answer 1

Step-by-step explanation:

We know that if a|ca|c and b|cb|c then a⋅b⋅s=ca⋅b⋅s=c (for some positive integer ss). (ab|c)(ab|c)

Then doesn't ab|dcab|dc since ab|cab|c?

I feel like I'm misunderstanding my givens.

Can we say lcm(a,b)=clcm⁡(a,b)=c, hcf(a,b)=dhcf⁡(a,b)=d, and lcd(a,b)hcf(a∗b)=a∗blcd⁡(a,b)hcf⁡(a∗b)=a∗b?

Thus, ab|dcab|dc as dc=abdc=ab.