A Congruential Identity and the 2-adic Order of Lacunary Sums of Binomial Coefficients
نویسندگان
چکیده
In this paper we obtain a universal lower bound on the 2-adic order of lacunary sums of binomial coefficients. By means of necessary and sufficient conditions, we determine the set of values for which the bound is achieved and show the periodicity of the set. We prove a congruential identity for the corresponding generating function. Our approach gives an alternative and transparent proof for some results derived recently by the second author and extends them. We also propose a conjecture that implies a recursion for calculating the 2-adic order of the lacunary sums for almost all values. A congruence in the style of Lucas is proved for the lacunary sums considered.
منابع مشابه
On the Order of Lacunary Sums of Binomial Coefficients
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My mathematical research interests are in number theory and algebraic geometry. My thesis work concerns the arithmetic of a family of rational numbers known as multiple harmonic sums, which are truncated approximations of multiple zeta values. I explore new structures underlying relations involving multiple harmonic sums, p-adic L-values, Bernoulli numbers, and binomial coefficients. This is us...
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