The Gelasian (Late Villanyan-MN17) diversified micromammal assemblage with Mimomys pliocaenicus from Coste San Giacomo (Anagni basin, central Italy), taxonomy and comparison with selected european sites

The Gelasian site of Coste San Giacomo (CSG) (central Italy) provides a unique opportunity to investigate the faunal and environmental changes occurred in Mediterranean Europe during the Early Pleistocene. The finding of both large and small mammal fauna has a great biochronological and palaeoenvironmental value. In this work the description of the small mammal assemblage is presented and discussed in detail for the first time. Twelve taxa, belonging to three orders, have been in fact identified and described (six Rodentia, one Lagomorpha and five Eulipotyphla). In particular, the CSG small mammal assemblage has provided the largest collection in Europe of Mimomys pliocaenicus and, for this reason, it can be considered as a reference. Finally, the occurrence of the Desmaninae subfamily is reported for the first time in Italy. © 2015 Associazione Teriologica Italiana

On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2

For an integer $k\geq 2$, let $\{F^{(k)}_{n} \}_{n\geq 0}$ be the $k$--generalized Fibonacci sequence which starts with $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $c$ having at least two presentations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$