Some of my new and almost new problems and results in combinatorial number theory

Chapters in this book

1. I-IV I
2. Preface V
3. Table of contents VII
4. List of participants XI
5. The average behaviour of the number of solutions of a Diophantine equation and an averaging technique 1
6. Pisot numbers and greedy algorithm 9
7. Upper bounds for the resultant and Diophantine applications 23
8. Logarithmic forms and the abc- conjecture 37
9. Local—global principles and linear algebraic groups 45
10. Diophantine approximation and quadratic fields 55
11. On a problem of P. Turán concerning irreducible polynomials 95
12. On products of the terms of linear recurrences 101
13. On the Kronecker-Győry specialization 107
14. On the greatest prime factor of axm + byn 115
15. The Euclidean algorithm in cubic number fields 123
16. A problem of Diophantus and Dickson's conjecture 147
17. Transcendence of Jacobi's theta series and related results 157
18. Some of my new and almost new problems and results in combinatorial number theory 169
19. Lower bounds for resultants II 181
20. Distribution of binomial coefficients modulo ρ 199
21. The distribution of the zeros of the Riemann zeta function and Baker's theorems 211
22. θ-congruent numbers 235
23. Computing power integral bases in algebraic number fields 243
24. Recent bounds for the solutions of decomposable form equations 255
25. On a generalization of the Maillet determinant 271
26. An approximation problem concerning linear recurrences 289
27. Elementary definability from Pascal's triangle modulo ρ and the set of e-th powers 295
28. New methods in algebraic independence 311
29. On the arithmetic of simplest sextic fields and related Thue equations 331
30. Algebraic constructions of lattices; isodual lattices 349
31. Real roots of Fibonacci-like polynomials 361
32. On some modular identities 371
33. Complete resolution of some families of Diophantine equations 383
34. Experiments on a problem of D. Shanks concerning quadratic fields 401
35. Squares in binary recurrence sequences 409
36. Algebraic curves over finite fields with many rational points 423
37. On a Shintani decomposition for a cubic field defined by X3 + kX - 1 = 0 445
38. Klein polyhedra for complete decomposable forms 453
39. Arithmetical progressions formed by Lucas pseudoprimes 465
40. Reducibility of polynomials over Kroneckerian fields 473
41. A note on certain exponential Diophantine equations 479
42. The fundamental lemma of Kubilius and the model of Kubilius in number fields 489
43. Diophantine properties of digital expansions 501
44. Exponential diophantine equations 1986-1996 523
45. Basic algorithms for elliptic curves 541