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Creators/Authors contains: "Sun, Yewen"

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  1. ; ; ( , Discrete Mathematics)
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  2. ; ; ; ; ; ; ; ( , Integers)
    In this paper, we investigate the existence of Sierpi´nski numbers and Riesel numbers as binomial coefficients. We show that for any odd positive integer r, there exist infinitely many Sierpi´nski numbers and Riesel numbers of the form kCr. Let S(x) be the number of positive integers r satisfying 1 ≤ r ≤ x for which kCr is a Sierpi´nski number for infinitely many k. We further show that the value S(x)/x gets arbitrarily close to 1 as x tends to infinity. Generalizations to base a-Sierpi´nski numbers and base a-Riesel numbers are also considered. In particular, we prove that there exist infinitely many positive integers r such that kCr is simultaneously a base a-Sierpi´nski and base a-Riesel number for infinitely many k. 
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