On solutions of the Diophantine equation $L_n\pm L_m=p^a$

Lucas sequence is one of the most studied binary recurrence sequence defined by the relation $L_{n+2}=L_{n+1}+L_n;~L_0=2, L_1=1$. In this paper, we investigate all the sums and differences of two Lucas numbers that are powers of a odd prime $p$ satisfying $p<10^3$.