Geodesic
Congruences for a class of alternating lacunary sums of binomial coefficients
Journal of integer sequences, Tome 10 (2007) no. 10
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.
Classification : 11A07, 05A19, 11B65
Keywords: binomial sums, binomial coefficients, congruences 
@article{JIS_2007__10_10_a1,
     author = {Dilcher,  Karl},
     title = {Congruences for a class of alternating lacunary sums of binomial coefficients},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {10},
     zbl = {1174.11002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_10_a1/}
}
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Dilcher,  Karl. Congruences for a class of alternating lacunary sums of binomial coefficients. Journal of integer sequences, Tome 10 (2007) no. 10. http://geodesic.mathdoc.fr/item/JIS_2007__10_10_a1/