Mihoubi, Miloud; Taharbouchet, Said Identities and congruences involving the geometric polynomials. (English) Zbl 1438.05015 Miskolc Math. Notes 20, No. 1, 395-408 (2019). Summary: In this paper, we investigate the umbral representation of the geometric polynomials \(\mathfrak{w}_{x}^{n}:=w_{n} (x) \) to derive some properties involving these polynomials. Furthermore, for any prime number \(p\) and any polynomial \(f\) with integer coefficients, we show \( (f (\mathfrak{w}_{x}))^{p}\equiv f(\mathfrak{w}_{x}) \pmod p\) and we give other curious congruences. Cited in 5 Documents MSC: 05A18 Partitions of sets 05A40 Umbral calculus 11A07 Congruences; primitive roots; residue systems Keywords:geometric umbra; geometric polynomials; identities; congruences PDFBibTeX XMLCite \textit{M. Mihoubi} and \textit{S. Taharbouchet}, Miskolc Math. Notes 20, No. 1, 395--408 (2019; Zbl 1438.05015) Full Text: DOI