Here the factor ε, corresponding to the prime 2, is 1 if "a" + "b" is odd and 2 if "a" + "b" is even. The first product index "p" runs over the finitely-many odd primes dividing both "a" and "b". For these primes formula_10 since "p" then cannot divide "c". The second product index formula_11 runs over the infinitely-many odd primes not dividing "a". For these primes formula_8 equals 1, 2, or 0 depending on whether the discriminant is 0, a non-zero square, or a non-square modulo "p". This is accounted for by the use of the Legendre symbol, formula_13. When a prime "p" divides "a" but not "b" there is one root modulo "p". Consequently, such primes do not contribute to the product.