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Class groups, totally positive units, and squares
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
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On unit solutions of the equation xyz = x + y + z in totally imaginary quartic fields
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.
A Number Field Without Any Integral Basis
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Classes of equations of the type $y^{2}=x^{3}+k$ having no rational solutions
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
Advanced Problems: 5736,5746-5752
Some contributions to the theory of cyclic quartic extensions of the rationals
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 paperExpand
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