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Coprime mappings between sets of consecutive integers

Published online by Cambridge University Press:  26 February 2010

D. E. Daykin  and
M. J. Baines
D. E. Daykin
Affiliation:
The University, Reading
M. J. Baines
Affiliation:
The University, Reading
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Extract

Let

be two sets of n ≥ 1 consecutive integers with s ≤ t. In this note we are concerned with one-to-one mappings of Γ onto II. If i → f(i) is such a mapping then for i ∈ Γ we write Fi for the highest common factor (i, f(i)), and if Fi = 1 for all i ∈ Γ we say that f is a coprime mapping. Our principal result is

THEOREM 1. If Γ = {1, 2, …, n} and Π = {n+1, n+2, …, 2n} then a one-to-one coprime mapping of Γ onto II can be constructed.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 2 , December 1963 , pp. 132 - 136
Copyright
Copyright © University College London 1963

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References

1.Fraenkel, A. A., “Integers and theory of numbers”, Scripta Mathematica, New York, 1955.Google Scholar