ZOUAREG YAHIA2022-09-042022-09-042022http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/31325Heim and Neuhauser investigated some polynomials related to the Dedekind function. They proved the log-concavity of these polynomials and conjectured that they have only real zeros. In this thesis, we prove this conjecture, and deduce some identities for Fibonacci numbers and determine the modes of another sequence related to Fibonacci polynomials. We have also studied solution of some diophantine equations.Diophantine equations. Log–concave. Polynomial. Sequence. Zeros. RThesis