I believe since they give you what b is you can simply substitute n/gcf(n,a) in for b and see if it fulfills those two conditions, which it does.
Im new and working on a proof - well actually i cant even start this proof.
If gcf (n,a) >1 prove there exists b not equal unto 0 mod n but a*b = 0 mod n.
Im even told that b = n/gcf(n,a)
any ideas or help will surely be appreciated and allow me to actually spend time with my family instead of staring at this problem for 4 hours getting nowhere.....