gausss class number problem

Input interpretation

Gauss's class number problem

Definition

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d) = m. Heegner gave a solution for m = 1, but it was not completely accepted due to a number of apparent gaps. However, subsequent examination of Heegner's proof showed it to be "essentially" correct. Conway and Guy therefore call the nine values of n(-d) having h(-d) = 1 where -d is the binary quadratic form discriminant corresponding to an quadratic field a + b sqrt(n) (n = - 1, -2, -3, -7, -11, -19, -43, -67, and -163; OEIS A003173) the Heegner numbers. The Heegner numbers have a number of fascinating properties.
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