|
|
A031398
|
|
Squarefree n with no 4k+3 factors such that Pell equation x^2 - n y^2 = -1 is insoluble.
|
|
7
|
|
|
34, 146, 178, 194, 205, 221, 305, 377, 386, 410, 466, 482, 505, 514, 545, 562, 674, 689, 706, 745, 793, 802, 866, 890, 898, 905, 1154, 1186, 1202, 1205, 1234, 1282, 1345, 1346, 1394, 1405, 1469, 1513, 1517, 1537, 1538, 1717, 1762, 1802, 1858
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Or, numbers n which are the sum of two relatively-prime squares but for which x^2 - n*y^2 does not represent -1.
|
|
REFERENCES
|
Harvey Cohn, "Advanced Number Theory".
|
|
LINKS
|
|
|
MATHEMATICA
|
sel = Select[Range[2000], SquareFreeQ[#] && FreeQ[Mod[FactorInteger[#][[All, 1]], 4], 3]&]; r[n_] := Reduce[x^2-n*y^2 == -1, {x, y}, Integers]; Reap[For[n=1, n <= Length[sel], n++, an = sel[[n]]; If[r[an] === False, Print[an]; Sow[an]]]][[2, 1]] (* Jean-François Alcover, Feb 04 2014 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|