On the Diophantine equation x 2 + p 2 k + 1 = 4 y n

S. Akhtar Arif and Amal S. Al-Ali

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-5

Abstract:

It has been proved that if p is an odd prime, y > 1 , k ≥ 0 , n is an integer greater than or equal to 4 , ( n , 3 h ) = 1 where h is the class number of the field Q ( − p ) , then the equation x 2 + p 2 k + 1 = 4 y n has exactly five families of solution in the positive integers x , y . It is further proved that when n = 3 and p = 3 a 2 ± 4 , then it has a unique solution k = 0 , y = a 2 ± 1 .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:962050

DOI: 10.1155/S0161171202106107

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