id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4702	Tadee, Suton; Siraworakun, Apirat	Non-existence of Positive Integer Solutions of the Diophantine Equation $p^x+(p+2q)^y=z^2$, where $p$, $q$ and $p+2q$ are Prime Numbers	2023	12	.pdf	application/pdf	5382	416	90	If p is a prime number with 2q ̸≡ 1 (mod p) and satisfies any of the following conditions: (i) p ≡ q2 + 8n1r S2 (mod 8q), (ii) p ≡ − q2 + 8n1r S2 (mod 8q), (iii) p ≡ 3q2 + 8n1r S1 (mod 8q), or (iv) p ≡ − 3q2 + 8n1r S1 (mod 8q), where S1 ∈ {2, 4, 6, . . If p satisfies any of the following conditions: (i) p ≡ q2 + 32n0n1r S2 (mod 8q), (ii) p ≡ − q2 + 32n0n1r S1 (mod 8q), (iii) p ≡ 3q2 + 32n0n1r S2 (mod 8q), or (iv) p ≡ − 3q2 + 32n0n1r S1 (mod 8q), where S1 ∈ {2, 4, 6, . . .	cache/ejpam-4702.pdf	txt/ejpam-4702.txt