id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6593	Bacani, Jerico Bravo; Avenilla, Merlyn	On the Diophantine Equation $p^x + (p + 5k)^y = z^2$	2025	24	.pdf	application/pdf	11954	735	93	Finding for q we have, q = z2 − 22+4n = (z − 21+2n)(z + 21+2n). Math, 18 (3) (2025), 6593 23 of 24 There are finitely many solutions when y = 1 and x = 2 + 4n, n ∈ N0, where the value of k and z are given by k = (22+2n − 1)/5 and z = (5k + 3)/2.	cache/ejpam-6593.pdf	txt/ejpam-6593.txt