Estimates of the least prime factor of a binomial coefficient

Authors:
P. Erdős, C. B. Lacampagne and J. L. Selfridge

Journal:
Math. Comp. **61** (1993), 215-224

MSC:
Primary 11B65; Secondary 11N37

DOI:
https://doi.org/10.1090/S0025-5718-1993-1199990-6

MathSciNet review:
1199990

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Abstract: We estimate the least prime factor *p* of the binomial coefficient for . The conjecture that is supported by considerable numerical evidence. Call a binomial coefficient **good** if . For write , where contains just those prime factors , and define the **deficiency** of a good binomial coefficient as the number of *i* for which . Let be the least integer such that is good. The bound is proved. We conjecture that our list of 17 binomial coefficients with deficiency is complete, and it seems that the number with deficiency 1 is finite. All with positive deficiency and are listed.

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1199990-6

Article copyright:
© Copyright 1993
American Mathematical Society