if "d" is a square-free integer (a product of distinct primes) other than 1, then q() is a quadratic extension of q. if "d" < 0, then the class number of the ring "r" of algebraic integers of q() is equal to 1 for precisely the following values of "d": "d" = −1, −2, −3, −7, −11, −19, −43, −67, and −163. this result was first conjectured by gauss and proven by kurt heegner, although heegner's proof was not believed until harold stark gave a later proof in 1967. (see stark-heegner theorem.) this is a special case of the famous class number problem.