Remarks on Fermat quotient operators over function fields

A study on QnQn-quotients and Fermat quotients over function fields was initially undertaken in a previous paper [6] by J. Sauerberg and L. Shu (1997). In this note, we revisit them and further investigate the properties of two closely-related quotients. Then, we provide interesting problems by making conjectures related to the Fermat quotients.