Samuel A. Hambleton

Generalized lucas-lehmer tests using Pell conics

Pell conics are used to write a Proth-Riesel twin-primality test. We discuss easy-to-find primality certificates for integers of the form m h±1. The known primality test for 3 h ± 1 is associated with X + 3Y = 4.

Pell conics and quadratic reciprocity

We give a proof of quadratic reciprocity, based on the arithmetic of conics. The proof works in all cases, and the calculations are remarkably simple.