A107998 Squarefree integers m for which the fundamental unit of Q(sqrt(m)) is of the form u + v*sqrt(m) for integer u, v.
2, 3, 6, 7, 10, 11, 14, 15, 17, 19, 22, 23, 26, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 55, 57, 58, 59, 62, 65, 66, 67, 70, 71, 73, 74, 78, 79, 82, 83, 86, 87, 89, 91, 94, 95, 97, 101, 102, 103, 105, 106, 107, 110, 111, 113, 114, 115, 118, 119, 122, 123, 127
Offset: 1
Keywords
References
- H. C. Williams, Eisenstein's problem and continued fractions, Utilitas Math. 37 (1990) 145-157.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..1000
- F. Arndt, Beiträge zur Theorie der quadratischen Formen, Archiv der Mathematik und Physik 15 (1850) 467-478.
- A. Cayley, Note sur l'équation x^2 - D*y^2 = +-4, D=5 (mod 8), J. Reine Angew. Math. 53 (1857) 369-371.
- Steven R. Finch, Class number theory
- Steven R. Finch, Class number theory [Cached copy, with permission of the author]
- Eric Weisstein's World of Mathematics, Fundamental unit
Crossrefs
Cf. A107997.
Programs
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Mathematica
Select[ Range[2, 127], (fu = NumberFieldFundamentalUnits @ Sqrt[#]; SquareFreeQ[#] && IntegerQ[fu[[1, 2, 1]] ] && IntegerQ[fu[[1, 2, 2]] ]) &] (* Jean-François Alcover, Jun 20 2013 *)