Let $$ A=\{1,2,\ldots,p-1\},\qquad B=\{1,2,\ldots,q-1\} $$ where $p,q$ are primes not necessarily distinct. Is there any elementary way to find the cardinal of the following set $$ AB=\{ab:\ a\in A,\ b\in B\} $$ and also the form of them. Thanks!