Congruences for a Class of Alternating Lacunary Sums of Binomial Coefficients
Karl Dilcher
Department of Mathematics and Statistics
Dalhousie University
Halifax, Nova Scotia B3H 3J5
Canada
Abstract:
An 1876 theorem of Hermite, later extended by Bachmann, gives congruences
modulo primes for lacunary sums over the rows of Pascal's triangle.
This paper gives an analogous result for alternating sums over a certain
class of rows. The proof makes use of properties of certain linear recurrences.
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(Concerned with sequences
A002620 and
A007318
.)
Received September 22 2007;
revised version received October 4 2007.
Published in Journal of Integer Sequences, October 5 2007.
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