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A254765 Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = A007522(n), n >=1 (primes congruent to 7 mod 8). 3

%I #11 Feb 14 2015 23:44:54

%S 1,1,3,1,5,1,3,7,3,1,7,9,1,5,7,3,5,1,9,11,7,1,9,5,11,13,11,3,7,17,11,

%T 1,7,13,3,1,7,13,5,15,21,11,7,13,5,9,1,17,23,1

%N Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = A007522(n), n >=1 (primes congruent to 7 mod 8).

%C For the corresponding term x1(n) see A254764(n).

%C See A254764 for comments and the Nagell reference.

%C The least positive y solutions (that is the ones of the first class) for the primes +1 and -1 (mod 8) together (including also prime 2) are given in A002335.

%F A254764(n)^2 - 2*a(n)^2 = A007522(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.

%e A254764(4)^2 - 2*a(4)^2 = 7^2 - 2*1^2 = 47 = A007522(4).

%Y Cf. A007522, A254764, A254766, A254929, A254760, A254761, A254762, A254763, A002335.

%K nonn,easy

%O 1,3

%A _Wolfdieter Lang_, Feb 12 2015

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