where "m" and "r" are non-negative integers. for the value is 1 since numerator and denominator are both empty products. although the formula in the first clause appears to involve a rational function, it actually designates a polynomial, because the division is exact in z<nowiki>[</nowiki>"q"<nowiki>]</nowiki>. note that the formula can be applied for , and gives 0 due to a factor in the numerator, in accordance with the second clause (for even larger "r" the factor 0 remains present in the numerator, but its further factors would involve negative powers of "q", whence explicitly stating the second clause is preferable). all of the factors in numerator and denominator are divisible by , with as quotient a "q" number: