Table of Contents A0a |
Alternative to Chinese Remainder Theory |
1. New Algorithm Involving Quadratic Residues (Part IVa)) |
2. New Algorithm Involving Quadratic Residues (Part IVb)) |
3. New Algorithm Involving Quadratic Residues (Part IVc)) |
4. New Algorithm Involving Quadratic Residues (Part IVd)) |
5. Expanded Algorithm Involving Quadratic Residues (Part Ia)) |
6. Expanded Algorithm Involving Quadratic Residues (Part Ib)) |
7. Expanded Algorithm Involving Quadratic Residues (Part Ic)) |
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Table of Contents A0b |
Diophantine Multiples |
1. The Diophantine General Equation x2 + D∑(y2) = z2 (Intro) |
2. The Diophantine General Equation x2 + Dy2 = z2 (Part I) |
2c. Comparison of Known Method with the New Diophantine Method (Part IC) |
3. The Diophantine General Equation x2 − Dy2 = z2 (Part II) |
4. The Diophantine Equation x2 + 2y2 = z2 (Part III) |
5. The Diophantine Equation x2 − 2y2 = z2 (Part IV) |
6. The Diophantine Equation x2 + 3y2 = z2 (Part V) |
7. The Diophantine Equation x2 − 3y2 = z2 (Part VI) |
8. The Diophantine Equation x2 + 5y2 = z2 (Part VII) |
9. The Diophantine Equation x2 − 5y2 = z2 (Part VIII) |
10. The Diophantine Equation x2 + 4y2 = z2 (Part IX) |
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11. The Diophantine Equation - Quadruples (Part I) |
12. The Diophantine Equation - Quadruples (Part II) |
13. The Diophantine Equation - Quadruples (Part III) |
14. The Diophantine Equation - Quadruples (Part IV) |
15. The Diophantine Equation - Quadruples (Part V) |
16. The Diophantine Equation - Quadruples (Part VI) |
17. The Diophantine Equation - Quintuples/Sextuples (Part X) |
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Table of Contents A1a |
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1. The Diophantine Equation 2y2 − x2 = z2 and Magic Squares (Part I) |
2. The Diophantine Equation 2y2 − x2 = z2 and Magic Squares (Part II) |
3. The Diophantine Equation 2y2 − x2 = z2 and Magic Squares (Part I/IIA) Random Access |
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Table of Contents A1b |
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1. A Novel Method for Multiplying Large Numbers |
2. The Column Addition Triangle (CAT) - A Pascal Δ Analogy (Part I) |
3. The Column Addition Triangle (CAT) and Polynomials (Part II) |
4. Triangles Exhibiting Ascending Diagonal Properties (Part III) |
5. Pascal Type Triangles(1,2) (Part I) |
6. Pascal Type Triangles(1,3) (Part II) |
7. The Fibonacci Type Sequences Triangle and their Ascending Diagonals (Part A) |
8. The Ascending Diagonals of a Fibonacci Type Sequences Triangle (Part B) |
9. Partition Numbers and Methods for Calculation |
10. Congruence of Numbers Raised to Some Power (Part I) |
11. Congruence of Numbers Raised to Some Power (Part II) |
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Table of Contents A1c |
1. Sequences from Quadratic Residues (Part I) |
2. Sequences from Quadratic Residues (Part II) |
3. Finite Sequences from Quadratic Residues (Part III) |
4. Sequences from Quadratic Residues (Part IV) |
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Table of Contents A1d |
The Pellian Equation |
1. Finding the Diophantine Equation x2 − Dy2 = ±z2 Given (x,y,z) (Part IX) |
2. The Pellian Equation x2 −Dy2 = 1 Revisited (Part I) |
3. The Pellian Equation x2 −Dy2 = ±1 Revisited (Part II) |
4. The Pellian Equation x2 −Dy2 = ±1 From a Sequence Sn (Part IIIA) |
5. The Pellian Equation x2 −Dy2 = ±1 Continuation (Part IIIB) |
6. The Pellian Equation x2 −Dy2 = 1 from the Sequence (n+1)2 − 1 (Part IV) |
7. The Pellian Equation x2 −Dy2 = 1 from the Sequence n(n+1)(Part V) |
8. The Pellian Equation x2 −Dy2 = 1 from a Paired Sequence P(n) (Part VI) |
9. The Pellian Equation x2 −Dy2 = 1 from a new Paired Sequence P(n) (Part VII) |
10. The Pellian Equation x2 −Dy2 = 1 from a Paired Sequences P(n) (Part VIII) |
11. The Pellian Equation x2 −Dy2 = 1 from a Paired Sequence P(n) (Part IX) |
12. The Pellian Equation x2 −Dy2 = 1 from two Paired Sequences (Part XA) |
13. The Pellian Equation x2 −Dy2 = 1 from two Paired Sequences (Part XB) |
14. The Pellian Equation x2 −Dy2 = 1 from two Paired Sequences (Part XC) |
15. The Pellian Equation x2 −Dy2 = 1 from two Paired Sequences (Part XD) |
16. The Pellian Equation x2 −Dy2 = 1 from two Paired Sequences (Part XE) |
17. The Pellian Equation x2 −Dy2 = 1 from Multiple Sequences (Part XFa) |
18. The Pellian Equation x2 −Dy2 = 1 from Multiple Sequences (Part XFb) |
19. The Pellian Equation x2 −Dy2 = 1 from a Paired Sequence P(n) (Part XI) |
20. The Pellian Equation x2 −Dy2 = 1 from a Paired Sequence P(n) (Part XIIA) |
21. The Pellian Equation x2 −Dy2 = 1 from a Paired Sequence P(n) (Part XIIB) |
22. Calculating the Convergents of x2 −Dy2 = ±1 via Programming (Part XIII) |
23. The Pellian Equation x2 −Dy2 = ±1 from the Sequence (n + 1)2 + 1 (Part XIV) |
24. The Pellian Equation x2 −Dy2 = ±1 from Dual Sequences (Part XV) |
25. The Pellian Equation x2 −Dy2 = −1 from a new Sequence Sn (Part XVI) |
26. The Pellian Equation x2 −Dy2 = 1 from a Sequence Sn (Part XVII) |
27. The Role of Triangular Numbers in the Pellian Equation x2 −Dy2 = 1 (Part XVIII) |
28. Consecutive Odd Numbers and the Pellian Equation (Part XIXA) |
29. Consecutive Odd Numbers and the Pellian Equation (Part XIXB) |
30. Triangular and the Odd Numbers and the Pellian Equation (Part XIXC) |
31. Triangular Numbers and the Pellian Equation x2 −Dy2 = 1 (Part XX) |
32. The Pellian Equation x2 −Dy2 = ±1 from Dual Sequences (Part XXI) |
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