What is the correct formula that wouldresult from the combination of the two ionic species?

In order to find which ionic compound will be made from these two ions, we need to match their charges:
NH4 has a +1 charge
N has a -3 charge
We will need 3 NH4 in order to match the -3 charge of N, therefore we will have a neutral compound:
(NH4)3N is the best option, this is Ammonium nitride