## On the ‘gap’ in a theorem of Heegner.(English)Zbl 0198.37702

Summary: In 1952, K. Heegner [Math. Z. 56, 227–253 (1952; Zbl 0049.16202)] gave a proof of the fact that there are exactly nine complex quadratic fields of class-number one. His proof rests on the fact that a certain 24th degree polynomial with rational coefficients has a 6th degree factor which also has rational coefficients. Unfortunately, this reducibility has never been justified. In this paper, we fill this gap in Heegner’s proof.