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WOLSTENHOLME’S THEOREM: ITS GENERALIZATIONS AND EXTENSIONS IN THE LAST HUNDRED AND FIFTY YEARS (1862–2012)
, 2011
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A Further Generalization of a Congruence of Wolstenhome
- JOURNAL OF INTEGER SEQUENCES, VOL. 15 (2012), ARTICLE 12.8.6
, 2012
"... Given a pair (Ut) and (Vt) of Lucas sequences, Kimball and Webb showed that ..."
Abstract
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Given a pair (Ut) and (Vt) of Lucas sequences, Kimball and Webb showed that
The congruence of Wolstenholme and generalized binomial coefficients related to Lucas Sequences
, 2014
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Congruences Involving Sums of Ratios of Lucas Sequences
"... Given a pair (Ut) and (Vt) of Lucas sequences, we establish various congruences involving sums of ratios Vt. More precisely, let p be a prime divisor of the positive Ut integer m. We establish congruences, modulo powers of p, for the sum ∑ Vt, where t Ut runs from 1 to r(m), the rank of m, and r(q) ..."
Abstract
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Given a pair (Ut) and (Vt) of Lucas sequences, we establish various congruences involving sums of ratios Vt. More precisely, let p be a prime divisor of the positive Ut integer m. We establish congruences, modulo powers of p, for the sum ∑ Vt, where t Ut runs from 1 to r(m), the rank of m, and r(q) ∤ t for all prime factors q of m.
