A107997 - OEIS

%I #33 Sep 04 2021 21:35:53

%S 5,13,21,29,53,61,69,77,85,93,109,133,149,157,165,173,181,205,213,221,

%T 229,237,253,277,285,293,301,309,317,341,357,365,397,413,421,429,437,

%U 445,453,461,469,493,501,509,517,533,541,565,581,589,597,613,629,645

%N 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.

%C 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.

%D E. L. Ince, Cycles of Reduced Ideals in Quadratic Fields, British Association Mathematical Tables, Vol. IV, London, 1934.

%D H. C. Williams, Eisenstein's problem and continued fractions, Utilitas Math. 37 (1990) 145-157.

%H Robert G. Wilson v, <a href="/A107997/b107997.txt">Table of n, a(n) for n = 1..1000</a> (first 161 terms from Charles R Greathouse IV)

%H F. Arndt, <a href="https://www.digitale-sammlungen.de/en/view/bsb10593875?page=524,525">Beiträge zur Theorie der quadratischen Formen</a>, Archiv der Mathematik und Physik 15 (1850) 467-478.

%H A. Cayley, <a href="https://www.digizeitschriften.de/dms/img/?PID=GDZPPN002149834">Note sur l'équation x^2 - D*y^2 = +-4, D=5 (mod 8)</a>, J. Reine Angew. Math. 53 (1857) 369-371.

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Class number theory</a>

%H Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FundamentalUnit.html">Fundamental unit</a>

%t 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 *)

%Y Cf. A107998.

%K nonn

%O 1,1

%A _Steven Finch_, Jun 13 2005