Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 393.10005
Autor: Ecklund, E.F.jun.; Eggleton, R.B.; Erdös, Paul; Selfridge, J.L.
Title: On the prime factorization of binomial coefficients. (In English)
Source: J. Aust. Math. Soc., Ser. A 26, 257-269 (1978).
Review: Let n and k be positive integers such that n \geq 2k. If \binom{n}{k} = uv where each prime factor of u is less than k and each prime factor of v is greater than or equal to k, it is proved here that u < v except for twelve cases which are listed. It is also shown that if \binom{n}{k} = UV where each prime factor of U is less than or equal to k and each prime factor of V exceeds k, then U < V with finitely may exceptions. Nineteen such exceptions are given and it is conjectured that there are no others. The arguments used are elementary but not simple.
Reviewer: P.Hagis
Classif.: * 11A41 Elemementary prime number theory
05A10 Combinatorial functions
Keywords: prime factorization; binomial coefficients
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