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. Finding x and y which give small multiples k in x2 - dy2 = kn;
  4. Solving the Pell equation x2 - dy2 = ±1 by the nearest integer continued fraction method (NICF);
  5. Solving the Pell equation x2 - dy2 = ±1 by the nearest square continued fraction method (NSCF);
  6. Solving the Pell equations x2 - dy2 = ±1, ±2, ±3 and ± 4;
  7. The Grytczuk, Luca, Wojtowicz construction of non-square d such that the negative Pell equation is soluble;
  8. Testing the solublity of the negative Pell equation x2 - Dy2 = -1, D > 1 and not a perfect square;
  9. Finding the fundamental unit of a real quadratic field;
  10. Expressing a prime p=4n+1 as a sum of two squares;
  11. Solving the diophantine equation ax2+by2=m using Cornacchia's method;
  12. Solving the diophantine equation ax2+bxy+cy2=m, (d = b2 - 4ac < 0, a > 0, c > 0).

Last modified 2nd November 2006
Return to main page