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On Binomial Coefficient Residues

Published online by Cambridge University Press:  20 November 2018

J . B. Roberts
J . B. Roberts*
Affiliation:
Wesleyan University, Middletown, Conn.
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The number of binomial coefficients , which are congruent to j , 0 ≤ j ≤ p − 1, modulo the prime number p is denoted by θj(n). In this paper we give systems of simultaneous linear difference equations with constant coefficients whose solutions would yield the quantities θj(n) explicitly.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 363 - 370
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Dickson, L. E., History of the Theory of Numbers, vol.1 (Chelsea, New York, 1952).Google Scholar
2. Glaisher, J. W. L., On the residue of a binomial theorem coeffcient with respect to a prime modulus, Quart. J. Math., 30 (1899), 150–156.Google Scholar
3. Vinogradoff, I. M., An Introduction to the Theory of Numbers, (London and New York, Pergamon Press, 1955).Google Scholar