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- Title
Non-existence of Positive Integer Solutions of the Diophantine Equation p<sup>x</sup> + (p + 2q)<sup>y</sup> = z², where p, q and p + 2q are Prime Numbers.
- Authors
Tadee, Suton; Siraworakun, Apirat
- Abstract
The Diophantine equation px + (p + 2q)y = z², where p, q and p + 2q are prime numbers, is studied widely. Many authors give q as an explicit prime number and investigate the positive integer solutions and some conditions for non-existence of positive integer solutions. In this work, we gather some conditions for odd prime numbers p and q for showing that the Diophantine equation px + (p + 2q)y = z² has no positive integer solution. Moreover, many examples of Diophantine equations with no positive integer solution are illustrated.
- Subjects
PRIME numbers; DIOPHANTINE equations; CHINESE remainder theorem; INTEGERS; ODD numbers
- Publication
European Journal of Pure & Applied Mathematics, 2023, Vol 16, Issue 2, p724
- ISSN
1307-5543
- Publication type
Article
- DOI
10.29020/nybg.ejpam.v16i2.4702