Quadratic diophantine equations and fundamental unit BCMATH programs

  1. Solving x2 – dy2 = n, d > 0, by the Lagrange-Mollin-Matthews method;

  2. Solving ax2+bxy+cy2 = n, (d = b2 – 4ac > 0, d non-square) by the Lagrange-Matthews method;

  3. Solving ax2-by2 = ±1.

  4. Finding x and y which give small multiples k in x2 – dy2 = kn;

  5. Solving the Pell equation x2 – dy2 = ± 1 by the nearest integer continued fraction method (NICF-H) not using midpoint criteria;

  6. Solving the Pell equation x2 – dy2 = ± 1 by the nearest integer continued fraction method (NICF-P), using midpoint criteria;

  7. Solving the Pell equation x2 – dy2 = ± 1 by the nearest square continued fraction method (NSCF) not using midpoint criteria;

  8. Solving the Pell equation x2 – dy2 = ± 1 by the nearest square continued fraction method (NSCF), using midpoint criteria;

  9. Solving the diophantine equation x2–xy–(D–1)/4y2=± 1 using the nearest square continued fraction of (1+√D)/2, D≡ 1(mod 4);

  10. Solving the Pell equations x2 – dy2 = ± 1, ± 2, ± 3 and ± 4;

  11. The Grytczuk, Luca, Wojtowicz construction of non-square d such that the negative Pell equation is soluble;

  12. Finding the fundamental unit of a real quadratic field;

  13. Expressing a prime p=4n+1 as a sum of two squares;

  14. Solving the diophantine equation ax2+by2=m using Cornacchia's method;

  15. Solving the diophantine equation ax2+bxy+cy2=m, (d = b2 – 4ac < 0, a > 0, c > 0).

Last modified 8th May 2012
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