Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-19T06:29:03.762Z Has data issue: false hasContentIssue false
  • English
  • Français

Proof of D. J. Newman's coprime mapping conjecture

Published online by Cambridge University Press:  26 February 2010

Carl Pomerance  and
J. L. Selfridge
Carl Pomerance
Affiliation:
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 and University of Georgia, Athens, Georgia 30602.
J. L. Selfridge
Affiliation:
Mathematical Reviews, Ann Arbor, Michigan 48109 and Northern Illinois University, Dekalb, Illinois 60115
Get access

Extract

In this paper we prove

Theorem 1. If N is a natural number and I is an interval of N consecutive integers, then there is a 1–1 correspondencef: {1, 2,…, N} → I such that (i, f(i)) = 1 for 1 ≤ i ≤ N.

Type
Research Article
Information
Mathematika , Volume 27 , Issue 1 , June 1980 , pp. 69 - 83
Copyright
Copyright © University College London 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Chvátal, V.. “A remark on Newman's conjecture”, Proc. Washington State Univ. Conf. on Number Theory, 1971, 113–129.Google Scholar
2.Daykin, D. E. and Baines, M. J.. “Coprime mappings between sets of consecutive integers”, Mathematika, 10 (1963), 132–136.CrossRefGoogle Scholar
3.Erdös, P.. “Some remarks about additive and multiplicative functions”, Bull. Amer. Math. Soc, 52 (1946), 527–537.CrossRefGoogle Scholar
4.Rosser, L J. B. and Schoenfeld, L.. “Approximate formulas for some functions of prime numbers”, Illinois J. Math., 6 (1962), 64–94.CrossRefGoogle Scholar