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A note on Carmichael numbers in residue classes

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Number Theory and Combinatorics
This chapter is in the book Number Theory and Combinatorics

Abstract

Improving on some recent results of Matomäki and of Wright, we show that the number of Carmichael numbers to X in a coprime residue class exceeds X1/(6 log log log X) for all sufficiently large X depending on the modulus of the residue class.

Abstract

Improving on some recent results of Matomäki and of Wright, we show that the number of Carmichael numbers to X in a coprime residue class exceeds X1/(6 log log log X) for all sufficiently large X depending on the modulus of the residue class.

Chapters in this book

  1. Frontmatter I
  2. Foreword V
  3. Contents VII
  4. Multivariate difference Gončarov polynomials 1
  5. On an inequality in a 1970 paper of R. L. Graham 21
  6. Arithmetic progressions in sumsets of sparse sets 27
  7. Multidimensional Padé approximation of binomial functions: equalities 35
  8. Graphical enumeration and stained glass windows, 1: rectangular grids 65
  9. Two extensions of Hilbert’s cube lemma 99
  10. The Gallai–Ramsey number for a tree versus complete graphs 109
  11. On Levine’s notorious hat puzzle 115
  12. Recurrence ranks and moment sequences 167
  13. On weak twins and up-and-down subpermutations 187
  14. Distance graphs and arithmetic progressions 203
  15. Consecutive primes which are widely digitally delicate 209
  16. Spanning trees and domination in hypercubes 249
  17. Rook domination on hexagonal hexagon boards 259
  18. Strongly image partition regular matrices 267
  19. Introducing shift-constrained Rado numbers 285
  20. Mertens’ prime product formula, dissected 297
  21. Curious convergent series of integers with missing digits 311
  22. A note on Carmichael numbers in residue classes 321
  23. Tilted corners in integer grids 329
  24. Remembrances 339
  25. A selected bibliography of Ron Graham 355
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https://doi.org/10.1515/9783110754216-019

Chapters in this book

  1. Frontmatter I
  2. Foreword V
  3. Contents VII
  4. Multivariate difference Gončarov polynomials 1
  5. On an inequality in a 1970 paper of R. L. Graham 21
  6. Arithmetic progressions in sumsets of sparse sets 27
  7. Multidimensional Padé approximation of binomial functions: equalities 35
  8. Graphical enumeration and stained glass windows, 1: rectangular grids 65
  9. Two extensions of Hilbert’s cube lemma 99
  10. The Gallai–Ramsey number for a tree versus complete graphs 109
  11. On Levine’s notorious hat puzzle 115
  12. Recurrence ranks and moment sequences 167
  13. On weak twins and up-and-down subpermutations 187
  14. Distance graphs and arithmetic progressions 203
  15. Consecutive primes which are widely digitally delicate 209
  16. Spanning trees and domination in hypercubes 249
  17. Rook domination on hexagonal hexagon boards 259
  18. Strongly image partition regular matrices 267
  19. Introducing shift-constrained Rado numbers 285
  20. Mertens’ prime product formula, dissected 297
  21. Curious convergent series of integers with missing digits 311
  22. A note on Carmichael numbers in residue classes 321
  23. Tilted corners in integer grids 329
  24. Remembrances 339
  25. A selected bibliography of Ron Graham 355
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