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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.

%I A107998 #28 Aug 11 2025 07:17:10
%S A107998 2,3,6,7,10,11,14,15,17,19,22,23,26,30,31,33,34,35,37,38,39,41,42,43,
%T A107998 46,47,51,55,57,58,59,62,65,66,67,70,71,73,74,78,79,82,83,86,87,89,91,
%U A107998 94,95,97,101,102,103,105,106,107,110,111,113,114,115,118,119,122,123,127
%N 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.
%D A107998 H. C. Williams, Eisenstein's problem and continued fractions, Utilitas Math. 37 (1990) 145-157.
%H A107998 Robert G. Wilson v, <a href="/A107998/b107998.txt">Table of n, a(n) for n = 1..1000</a>
%H A107998 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 A107998 A. Cayley, <a href="https://gdz.sub.uni-goettingen.de/id/PPN243919689_0053">Note sur l'équation x^2 - D*y^2 = +-4, D=5 (mod 8)</a>, J. Reine Angew. Math. 53 (1857) 369-371.
%H A107998 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Class number theory</a>
%H A107998 Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%H A107998 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FundamentalUnit.html">Fundamental unit</a>
%t A107998 Select[ Range[2, 127], (fu = NumberFieldFundamentalUnits @ Sqrt[#]; SquareFreeQ[#] && IntegerQ[fu[[1, 2, 1]] ] && IntegerQ[fu[[1, 2, 2]] ]) &] (* _Jean-François Alcover_, Jun 20 2013 *)
%Y A107998 Cf. A107997.
%K A107998 nonn
%O A107998 1,1
%A A107998 _Steven Finch_, Jun 13 2005