This is a program for finding the least solutions of diophantine equations x^{2} - dy^{2} = ±1, ±2, ±3 and the least primitive solutions of x^{2} - dy^{2} = ±4.

The algorithm is based on K. Rosen, *Elementary number theory and its applications*, p.382,

B.A. Venkov, *Elementary Number Theory*, p.62 and
D. Knuth, *Art of computer programming*, Vol.2, p.359.

Also see L. Holzer, *Zahlentheorie*, Kap. 38, Satz 9, Seite 171,
which states that if d > 2, then no two of
x^{2} - dy^{2} = -1,
x^{2} - dy^{2} = -2,
x^{2} - dy^{2} = 2,
are simultaneously soluble.

e=1 prints the complete quotients (P+√d)/Q and partial quotients of the period of ⌊√d⌋+√d.

*Last modified 26th November 2003*

Return to main page