I want to create a PRNG for an integer only (with a max of 32767) system and tried to use an LCG. So I've chosen as $m = 32767$ and $c = 3$ and I tried to figure out a good $a$. However for the full period I have to choose $a = 32768$ which cannot be used since the maximum is 32767.
Can anyone help me creating a "good" LCG?
Another question: Since the maximum (could be / is) 32767 I don't know how to calculate the successor because $a * y_{-1} + 3$ could become greater than 32767 and this is not allowed in the system. So should I use $a * (y_{-1} \mod ((32767+3)/a) + 3$ then?