On Diophantine Equations 2 x ± (2 k p ) y = z 2 and −2 x + (2 k 3) y = z 2

Yuan Li (), Torre Lloyd and Angel Clinton
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Yuan Li: Department of Mathematics, Winston-Salem State University, Winston-Salem, NC 27110, USA
Torre Lloyd: Department of Mathematics, Winston-Salem State University, Winston-Salem, NC 27110, USA
Angel Clinton: Department of Mathematics, Winston-Salem State University, Winston-Salem, NC 27110, USA

Mathematics, 2024, vol. 12, issue 24, 1-7

Abstract: In this paper, we solve three Diophantine equations: 2 x ± ( 2 k p ) y = z 2 and − 2 x + ( 2 k 3 ) y = z 2 with k ≥ 0 and prime p ≡ ± 3 ( mod 8 ) . We obtain all the non-negative integer solutions by using elementary methods and the database of elliptic curves in “The L-functions and modular forms database” (LMFDB).

Keywords: Catalan equation; elliptic curve (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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