I am horribly familiar with pushups, see sig
The abs are always used in a pushup, they hold up your midsection. Get into a pushup position, then relax your abs - you fall down.
It's just that if your hands are far from your body, more of the force of your weight goes through your middle and less through your hands, so that your abs must exert more force to balance.
Hands closer to your strenum, works triceps more. Hands spread wide, works pecs more. Hands forward, works abs more.
Once you can do 10 pushups or so, then for a real challenge and burn, put your hands together diamond-style. Do as many as you can. Then put your hands one hand's width apart, and pushups until you can do no more. Then another hand's width out, and so on.
Or you can do a regular pushup, then at the bottom hold for a ten count, do 3 full pushups, then hold at the bottom for a ten count, and so on.