The Congruence of Wolstenholme for Generalized Binomial Coefficients Related to Lucas Sequences

In recent years much research has been carried out on extending Wolstenholme classical congruence modulo the cube of a prime to higher prime powers. Here we show that this work can be done in much broader generality by replacing ordinary binomials by Luca.snornials, which are generalized binomial coefficients related to fundamental Lucas sequences. The paper builds on earlier work of Kimball and Webb in relation to the Fibonacci sequence and on recent work of the author related to congruences involving sums of quotients of Lucas sequences. The paper offers what may be a. surprising line of development for very classical congruences.