Pillai's Problem Involving Narayana's Cows Sequence and Padovan Sequence

Let $\left(N_n\right)_{n\ge0}$ be the Narayana's cows sequence and $\left(P_n\right)_{n\ge0}$ the Padovan sequence, the aims in this paper is to study and completely solve the exponential Diophantine equation $N_m - P_n = N_{m_1}-N_{n_1}$ where $m, n, m_1$ and $n_1$ are positive integers with $(m, n)\neq (m_1, n_1)$.