• Honam Mathematical Journal
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• v.46 no.4
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• pp.552-566
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• 2024

In this paper, we investigate the perfect powers that are the difference between Perrin numbers (R_k)_k≥0 and Padovan numbers (P_k)_k≥0. Hence, we solve the equations P_n = x^a, 2P_n = x^a, P_n - R_m = x^a, or R_n - P_m = x^a such that a ≥ 1 and 2 ≤ x ≤ 10 are positive integers and n, m, and k are non-negative integers.