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A107997
Squarefree integers m congruent to 5 modulo 8 such that the minimal solution of the Pell equation x^2 - m*y^2 = +-4 has both x and y odd.
5
5, 13, 21, 29, 53, 61, 69, 77, 85, 93, 109, 133, 149, 157, 165, 173, 181, 205, 213, 221, 229, 237, 253, 277, 285, 293, 301, 309, 317, 341, 357, 365, 397, 413, 421, 429, 437, 445, 453, 461, 469, 493, 501, 509, 517, 533, 541, 565, 581, 589, 597, 613, 629, 645
OFFSET
1,1
COMMENTS
Squarefree integers m for which the fundamental unit of Q(sqrt(m)) is of the form (u + v*sqrt(m))/2, where u and v are both odd.
REFERENCES
E. L. Ince, Cycles of Reduced Ideals in Quadratic Fields, British Association Mathematical Tables, Vol. IV, London, 1934.
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 (first 161 terms from Charles R Greathouse IV)
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
fQ[n_] := Block[{nffu = NumberFieldFundamentalUnits@ Sqrt@ n}, SquareFreeQ@ n && Denominator[ nffu[[1, 2, 2]]] > 1]; Select[ 8Range@ 81 - 3, fQ] (* Robert G. Wilson v, Dec 22 2014 *)
CROSSREFS
Cf. A107998.
Sequence in context: A004770 A191155 A107996 * A355461 A166095 A166090
KEYWORD
nonn
AUTHOR
Steven Finch, Jun 13 2005
STATUS
approved