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- Title
GENERALIZATIONS OF WOLSTENHOLME’S THEOREM VIA THE P-ADIC LOGARITHM.
- Authors
Lombaers, Peter
- Abstract
We use the p-adic logarithm to express the binomial coefficient (2p−1 p−1) in terms of harmonic sums, where p is an odd prime. We use the same logarithmic method on norms of cyclotomic integers to obtain several congruences. For example, we show: p−1∑ k=1 (−1)k−1 1 k (2k k) ≡ (1 − L2 p)(L2 p − 3) 2p mod p², where Lp is a the p-th Lucas number
- Subjects
LUCAS numbers; CYCLOTOMIC fields; LOGARITHMS; GENERALIZATION; BINOMIAL coefficients; INTEGERS
- Publication
Integers: Electronic Journal of Combinatorial Number Theory, 2020, Vol 20, p1
- ISSN
1553-1732
- Publication type
Article