Modular periodicity of binomial coefficients

Mattarei, Sandro (2006) Modular periodicity of binomial coefficients. Journal of Number Theory, 117 (2). pp. 471-481. ISSN 0022-314X

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We prove that if the signed binomial coefficient (-1)iki viewed modulo p is a periodic function of i with period h in the range 0⩽i⩽k, then k+1 is a power of p, provided h is not too large compared to k. (In particular, 2h⩽k suffices). As an application, we prove that if G and H are multiplicative subgroups of a finite field, with H<G, and such that 1-α∈G for all

α∈G⧹H, then G∪{0} is a subfield.

Keywords:Binomial coefficients, Congruence, Periodicity, Fermat curves over finite fields
Divisions:College of Science > School of Mathematics and Physics
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ID Code:18513
Deposited On:02 Feb 2017 18:57

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