A347300 Under Hypothesis(H) (a version of the Generalized Riemann Hypothesis) the only principal real quadratic fields with discriminant d = r^2 + 1 == 1 (mod 4) are the fields Q(sqrt(t)) where t is one of the six numbers listed here.

5, 17, 37, 101, 197, 677

Offset: 1

Author

N. J. A. Sloane, Aug 28 2021

Keywords

• nonn
• fini
• full

References

• Gilles Lachaud, On real quadratic fields, Bull. Amer. Math. Soc., 17:2 (1987), 307-311. See Theorem 3.2.

Crossrefs

Cf. A003173, A003174, A014602, A050950.