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A264439 The y 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

%I

%S 1,17,1,49,21287,1,23,97,1,48727,161,151,1,21387679,241,1826021057,1,

%T 11692649642023,7,337,3903396217,1,294125365483681,17,449,7,

%U 1994828801,1,6399911,4798348971487087,577,119,7867888313,1,437071,161131189369,721,273849896195263,20783,262759

%N The y 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).

%C The corresponding x2(n) value is given by A264438(n). The positive fundamental solution (x1(n), y1(n)) of the first class is given by (2*A261247(n), A261248(n)).

%C There is only one class of proper solutions for those D = D(n) = A264354(n) values leading to (x1(n), y1(n)) = (x2(n), y2(n)).

%e n=1: D(1) = 8, (2*2)^2 - 8*1^2 = +8. The first class positive fundamental solution was identical, thus there is only one class of proper solutions for D = 8.

%e n=5: D(5) = 124, (2*118521)^2 - 124*21287^2 = +8. The first class solution was (2*39)^2 - 124*7^2 = +8. Thus there are two classes, conjugated to each other for this D value.

%Y Cf. A264354, A261247 (x1/2), A261248 (y1), A264438 (x2/2), A263012 (odd D), A264349, A264350, A264351, A264353.

%K nonn

%O 1,2

%A _Wolfdieter Lang_, Nov 19 2015

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)