Journal of Integer Sequences, Vol. 10 (2007), Article 07.10.1

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


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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