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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.

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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