The congruence of Wolstenholme and generalized binomial coefficients related to Lucas sequences

Using generalized binomial coefficients with respect to fundamental Lucas sequences we establish congruences that generalize the classical congruence of Wolstenholme and other related stronger congruences.Comment: 23 page

Biomarkers of Nutrition for Development (BOND)—Iron Review

This is the fifth in the series of reviews developed as part of the Biomarkers of Nutrition for Development (BOND) program. The BOND Iron Expert Panel (I-EP) reviewed the extant knowledge regarding iron biology, public health implications, and the relative usefulness of currently available biomarkers of iron status from deficiency to overload. Approaches to assessing intake, including bioavailability, are also covered. The report also covers technical and laboratory considerations for the use of available biomarkers of iron status, and concludes with a description of research priorities along with a brief discussion of new biomarkers with potential for use across the spectrum of activities related to the study of iron in human health. The I-EP concluded that current iron biomarkers are reliable for accurately assessing many aspects of iron nutrition. However, a clear distinction is made between the relative strengths of biomarkers to assess hematological consequences of iron deficiency versus other putative functional outcomes, particularly the relationship between maternal and fetal iron status during pregnancy, birth outcomes, and infant cognitive, motor and emotional development. The I-EP also highlighted the importance of considering the confounding effects of inflammation and infection on the interpretation of iron biomarker results, as well as the impact of life stage. Finally, alternative approaches to the evaluation of the risk for nutritional iron overload at the population level are presented, because the currently designated upper limits for the biomarker generally employed (serum ferritin) may not differentiate between true iron overload and the effects of subclinical inflammation

Density of prime divisors in linear-recurring sequences.

A general density theory of the set of prime divisors of linear recurring sequences with constant coefficients of any order is built up from the work of Lucas, Laxton, Hasse, and Lagarias. In particular, in this theory the notion of the rank of a prime divisor of a second order recurring sequence (Lucas), the group associated with a given recursion (Laxton), and the effective computation of densities (Hasse and Lagarias) are generalized and combined

On the Constant in the Average Digit Sum for a Recurrence-Based Numeration

International audienc

Divisibility of the middle Lucasnomial coefficient.

International audienc

Divisibility of Fibonomials and Lucasnomials via a general Kummer rule

International audienc

On functions expressible as words on a pair of Beatty sequences

International audienc