Proof of class number formulae by machine

Abstract

As an attempt to follow the direction of machine proof, a personal computer LE0386/25 is used to prove some class number formulae for certain imaginary quadratic number fields \({\Bbb Q}\left( {\sqrt p } \right)\),q=3, 7, 11, 19, 23, 31, 43 and 47) if the real quadratic number field \({\Bbb Q}\left( {\sqrt { - p} } \right)\) has class number one for a primep = 4N 2 + 1 (N is a positive integer).