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On the prime factorization of binomial coefficients

Published online by Cambridge University Press:  09 April 2009

E. F. Ecklund Jr ,
R. B. Eggleton ,
P. Erdös  and
J. L. Selfridge
E. F. Ecklund Jr
Affiliation:
Department of Computer Science Oregon State UniversityCorvallis, Organ 97330, USA
R. B. Eggleton
Affiliation:
Department of Mathematics The University of Newcastle New south Wales 2308, Australia
P. Erdös
Affiliation:
Hungarian Academy of Sciences Reáltanoda U. 13-15 Budapest V Hungary
J. L. Selfridge
Affiliation:
Department of Mathematical Sciences Northern Illnois UniversityDeKalb, Illnois 60115, USA
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Abstract

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For positive integers n and k, with n≥2k, let , where each prime factor of u is less than k, and each prime factor of v is at least equal to k. It is shown that u<v holds with just 12 exceptions, which are determined. If , where each prime factor of U is at most equal to k, and each prime factor of V is greater than k, then U<V holds with at most finitely many exceptions, 19 of which are determined. It is conjectured that there are no others.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 3 , November 1978 , pp. 257 - 269
Copyright
Copyright © Australian Mathematical Society 1978

References

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