Given a totally real algebraic number field K, we investigate when totally positive units, U?, are squares, u£. In particular, we prove that the rank of U? /Uji is bounded above by the minimum of (1)… Expand

Abstract It is determined when the equation u 1 u 2 u 3 = u 1 + u 2 + u 3 is solvable in the group of units of the ring of integers of a totally imaginary quartic field.

The equation y 2 = x 3 + k, k an integer, has been discussed by many authors. Mordell [1] has found many classes of k values for which the equation has no integral solutions. Fueter [2], Mordell [3]… Expand

Abstract K is a cyclic quartic extension of Q iff K = Q((rd + p d 1 2 ) 1 2 ) , where d > 1, p and r are rational integers, d squarefree, for which p2 + q2 = r2d for some integer q. Following a paper… Expand