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A264438 One-half of the x member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for even D(n) = A264354(n). 2
2, 45, 4, 235, 118521, 6, 156, 665, 8, 410581, 1431, 1464, 10, 217061235, 2629, 20578212225, 12, 143681684300109, 88, 4355, 53946009001, 14, 4149148875801021, 244, 6705, 108, 30839304871, 16, 103789115, 78990793279586649, 9775, 2068, 138751721731, 18, 7987764, 2984191388685, 13661, 5246209297401255, 406200, 5142295 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The corresponding y2(n) value is given by A264439(n). The positive fundamental solution (x1(n), y1(n)) of the first class is given by (2*A261247(n), A261248(n)).

There is only one class of proper solutions for those D = D(n) = A264354(n) that lead to (x1(n), y1(n)) = (x2(n), y2(n)).

See A264354 for comments and examples.

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

n=2: D(2) = 28, (2*45)^2 - 28*17^2 = +8. The first class solution was (2*3)^2 - 28*1^2 = +8. This is a D case with two classes of proper solutions.

n=3: D(3) = 56, (2*4)^2 - 56*1^2 = +8. The first class has the same solution, therefore this D has only one class of proper solutions.

CROSSREFS

Cf. A264354, A261247, A261248, A264439, A263012 (odd D), A264349, A264350, A264351, A264353.

Sequence in context: A161745 A048566 A321058 * A241762 A041241 A304015

Adjacent sequences:  A264435 A264436 A264437 * A264439 A264440 A264441

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Nov 19 2015

STATUS

approved

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)