where both a and b are positive integers that are of course smaller than n. But : n was the smallest number that can not be written as a product of primes . So it must be possible to write a and b as products of primes , because they are both smaller than n. But then the product
where both a and b are positive integers smaller than n. Since n is the smallest number which can not be written as a product of primes , both a and b can be written as products of primes .