Can i not claim my son as a dependent to get AOTC?

Hi,

after run the "trial" run, i found if I not claim my son on my tax return and if he file his own tax, we will get $500 more due to $1000 AOTC he may get. So can I do this legally?

Here is summery:

1. If I claim him, I still cannot get education tax credit due to my income is more than limit, >$180k. So I only get $500 as child tax credit.

2. If I do not claim him, I will loose $500 child tax credit only.

3. Now if he file himself with check the option "someone can claim him as dependent", but "did not claimed", he is getting $1000 for AOTC, even he do not have any income.

4. He got 1098-T on his name and we both get 1099-Q on our names, but the total eligible education is more than total of 1099-Q

 

So, can are we legally allowed to do this?