id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6452	Nilsrakoo, Weerayuth; Nilsrakoo, Achariya	Integral Representations of Generalizations of Pell Num-bers and their Companion Numbers	2025	18	.pdf	application/pdf	6305	403	82	Since ∆2 k = k2 + 4k − 4 = k2 + 4(k − 1) > 0 for k ≥ 2, this equation has two roots, r1 = k + ∆k 2 = σk and r2 = k − ∆k 2 = (k − ∆k) − k = 0. (4)	cache/ejpam-6452.pdf	txt/ejpam-6452.txt