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A264352 Exceptional even numbers D that do not admit a solution to the Pell equation X^2 - D Y^2 = +2. 3

%I

%S 82,146,178,226,274,434,466,514,562,578,626,658,818,914,994,1042,1106,

%T 1138,1202,1234,1394,1426,1522,1582,1618,1666,1714,1778,1874,1906,

%U 1918,2066,2098,2162,2194,2258,2306,2386,2402,2434,2482,2578,2642

%N Exceptional even numbers D that do not admit a solution to the Pell equation X^2 - D Y^2 = +2.

%C These are the even numbers D = 2*d with odd d having no prime factors 3 or 5 (mod 8), and do not represent +2 by the indefinite binary quadratic form X^2 - D*Y^2 (with discriminant 4*D > 0).

%C These even D numbers satisfy the necessary condition given in A261246. This condition is not sufficient as the present numbers show.

%C a(n)/2 = d(n) is 7 (mod 8) for n = 24, 31, 48, 55, 57, ...

%C The numbers D which admit solutions to the Pell equation X^2 - D Y^2 = +2 are given by A261246.

%C The exceptional odd D numbers are given in A263010.

%Y Cf. A261246,A263010, A261247, A261248.

%K nonn

%O 1,1

%A _Wolfdieter Lang_, Nov 12 2015

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)