first recall that the gcd of two integers can be written as a (in fact, the smallest) linear combination of the two integers.
also recall what it means for one integer to divide another. for some
you think you can get anywhere with those? or do you need another hint?
for 1 i'd start this way: all variables are integers here
Let and . You want to show that for some .
use the fact that to finish up.
for 2, since , we have that
you want to show that for some . use the fact that to accomplish this (start by translating that into an equation)