Entropy modulo a prime (Q2041579)

The author defines the entropy of a finite probability distribution in which the probabilities are integers modulo a prime \(p\). There is no logarithmic function mod \(p\) but the Fermat quotient provides an acceptable substitute. Some results are proved/mentioned including: (a) a characterization using a fundamental equation, and (b) properties similar to that for Shannon entropy. It appears that this new entropy is currently lacking a real application.