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Glaisher, J. W. L.

On the residue of a binomial-theorem coefficient with respect to a prime modulus. (English) JFM 29.0152.03

Quart. J. 30, 150-156 (1899).
JFM 29.0152.05

Cited in 3 Reviews
Cited in 18 Documents

MSC:

11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors
11B65 Binomial coefficients; factorials; \(q\)-identities

JFM Section:

Dritter Abschnitt. Niedere und höhere Arithmetik. Kapitel 2. Zahlentheorie. A. Allgemeines.

Keywords:

binomial coefficients

Citations:

JFM 29.0152.05
Cite Review PDF

Online Encyclopedia of Integer Sequences:

Gould’s sequence: a(n) = Sum_{k=0..n} (binomial(n,k) mod 2); number of odd entries in row n of Pascal’s triangle (A007318); a(n) = 2^A000120(n).
a(n) = OP(sum{i=0,...,n} OP(binomial(n,i))), where OP(n) is the odd part of n (A000265).