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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

F. Arndt, Beitrage zur Theorie der quadritischen Formen, Archiv der Mathematik und Physik 15 (1850) 467-478.

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

A. Cayley, Note sur l'equation x^2 - D*y^2 = +-4, D=5 (mod 8), J. Reine Angew. Math. 53 (1857) 369-371.

S. 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-Fran├žois Alcover, Jun 20 2013 *)

CROSSREFS

Cf. A107997.

Sequence in context: A188084 A242750 A299239 * A276884 A053438 A042964

Adjacent sequences:  A107995 A107996 A107997 * A107999 A108000 A108001

KEYWORD

nonn

AUTHOR

Steven Finch, Jun 13 2005

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)