A339882 Fundamental positive solution y(n) of the Diophantine equation x^2 - A045339(n)*y^2 = -2, for n >= 1.

1, 1, 1, 3, 9, 3, 27, 1, 3, 9, 747, 627, 153, 36321, 1, 121, 699, 537, 2900979, 43, 5843427, 803, 1, 59, 13809, 3, 12507, 541137, 11, 563210019, 57, 28906107, 55617, 3, 499, 212279001, 11516632737, 6633, 41281449, 33, 48957047673, 6284900361, 369485787, 3777

Offset: 1

Author

Wolfdieter Lang, Dec 22 2020

Keywords

• nonn

Comments

The corresponding x = x(n) values are given in A339881.

The conjecture is that all A045339 entries have solutions.

For details and examples [x(n), y(n)] see also A339881.

Crossrefs

Cf. A007520, A045339, A339881.

Formula

Generalized Pell equation. Fundamental solution a(n), with A339881(n)^2 - A045339(n)*a(n)^2 = -2, for n >= 1.