Products and sums of powers of binomial coefficients mod and solutions of certain quaternary Diophantine systems

Author:
Richard H. Hudson

Journal:
Math. Comp. **43** (1984), 603-613

MSC:
Primary 11D09; Secondary 11E20

DOI:
https://doi.org/10.1090/S0025-5718-1984-0758208-0

MathSciNet review:
758208

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Abstract: In this paper we prove that certain products and sums of powers of binomial coefficients modulo , , are determined by the parameters *x* occurring in distinct solutions of the quaternary quadratic partition

*K*and on the way that

*p*splits into prime ideals in the ring of integers of the field .

Let the four cosets of the subgroup *A* of quartic residues be given by , and let

*x*in the above partition of , in the complicated case that arises when the class number of

*K*is and .

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0758208-0

Article copyright:
© Copyright 1984
American Mathematical Society