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Congruences for a Class of Alternating Lacunary Sums of Binomial Coefficients
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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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