A108160 Squarefree integers m congruent to 5 modulo 8 such that the minimal solution of the Pell equation x^2 - m*y^2 = +-4 has both x and y even.

37, 101, 141, 197, 269, 349, 373, 381, 389, 485, 557, 573, 677, 701, 709, 757, 781, 813, 829, 877, 885, 901, 933, 973, 997, 1149, 1157, 1173, 1213, 1293, 1301, 1389, 1405, 1605, 1613, 1717, 1757, 1765, 1861, 1885, 1893, 1901, 1909, 1949, 1973, 2069, 2077, 2093

Offset: 1

Author

Steven Finch, Jun 13 2005

Keywords

• nonn

References

• C. F. Gauss, Disquisitiones Arithmeticae, Yale Univ. Press, 1966, section 256 VI, pp. 276-277.

Links

• Florian Breuer and James Punch, Quadratic units and cubic fields, arXiv:2507.06579 [math.NT], 2025. See p. 1.
• Arthur Cayley, Note sur l'équation x^2 - D*y^2 = +-4, D=5 (mod 8), J. Reine Angew. Math. 53 (1857) 369-371.
• Steven R. Finch, Class number theory [Cached copy, with permission of the author]
• Noburo Ishii, Pierre Kaplan and Kenneth S. Williams, On Eisenstein's problem, Acta Arith. 54 (1990) 323-345.

Crossrefs

Cf. A048941, A048942, A107997, A107999.

Extensions

More terms from Jinyuan Wang, Sep 08 2021