In Morocco, at the International Conference in Algebra, Number Theory and Their Applications,

we consider the Diophantine equation made up of linear recurrences and powers of primes. I will briefly outline results from students from B. Ha, L. McBeath, and L. Velasco in which they prove the existence of an effectively computable upper-bound on the non-negative integer solutions of a family of Diophantine equations, extending work of Pink and Ziegler, Mazumdar and Rout, Meher and Rout, and another result of Ziegler.