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

1,1

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

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 *)

Crossrefs

Cf. A107997.

Sequence in context: A242750 A299239 A335033 * A276884 A053438 A042964

Adjacent sequences: A107995 A107996 A107997 * A107999 A108000 A108001

Keyword

nonn

Author

Steven Finch, Jun 13 2005

Status

approved