Kim D, Koo JK, Hwan M.  Congruence equations of $ax^i+by^j\equiv c$ and $ax^i+by^j +d z^t \equiv c(\hbox {\rm mod}\, p)$ when $p=2q+1$ with $p$ and $q$ odd primes.  Commun. Korean Math. Soc. 2005;20:467-485.