Differences between elements of the same order in a finite field

In 1975, Michael Szalay showed that for any prime p>1019 and any integer δ with 1≤δ≤p−1, there exist at least two primitive roots g and h modulo p such that g−h≡δ(modp). Very recently, Brazelton, Harrington, Kannan and Litman have shown that for any n>6, there exists a prime p≡1(modn) for which there are two elements a and b of order n modulo p such that a−b≡1(modp). In this article, we extend these ideas to investigate arbitrary differences δ between elements of the same arbitrary order n modulo a prime p≡1(modn). Moreover, we show how all elements of a specific order n can be derived from a single fixed difference δ. Finally, we deduce a result concerning the differences between primitive roots for certain primes p≡3(mod4).