You can express the GCD as . More over, it is the smallest positive integer of this form.
Divide each side by d This looks like the expression of a GCD. You can be sure it is because 1 is the smallest positive integer you can get.
For number 2 you can use the fact that they have no common factors.
For the "cool" writting, you should learn Latex script. Double-click on the things other people wrote to see how it is. With some time you should learn.