摘要
In 1875, E. Lucas asked if the Diophantine equation 6Y^2= X(X+1)(2X+1) (1) has only the nontrivial solution X= 24, Y=70. This was solved by Watson in 1918 by using elliptic functions, and its proof is complicated (Messenger of Math., 48(1918/19), 1—22).A new proof based upon arithmetical considerations has been given by Ljunggren. In 1952, he used the Pell equation in a quadratic field, and for the fundamental unit in a quartic field he investi-
