On a theorem of Morlaye and Joly and its generalization

Ioulia N. Baoulina

doi:10.1016/j.ejc.2018.02.001

paper

On a theorem of Morlaye and Joly and its generalization

arXiv:1707.00353 · doi:10.1016/j.ejc.2018.02.001

Abstract

We show that a weaker version of the well-known theorem of Morlaye and Joly on diagonal equations is a simple consequence of a restricted variable version of the Chevalley-Warning theorem. Moreover, we extend the result of Morlaye and Joly to the case of an equation of the form $b_{1} D_{m_{1}} (X_{1}, a_{1}) + \dots + b_{n} D_{m_{n}} (X_{n}, a_{n}) = c,$ where $D_{m_{1}} (X_{1}, a_{1}), \dots, D_{m_{n}} (X_{n}, a_{n})$ are Dickson polynomials.

7 pages; Example 1 and reference [5] added