On the Diophantine equation x2+p2k+1=4yn

• Published in: International journal of mathematics and mathematical sciences Vol. 31; no. 11; pp. 695 - 699
• Main Authors: Arif, S Akhtar, Al-Ali, Amal S
• Format: Journal Article
• Language: English
• Published: Wiley 01.01.2002

It has been proved that if p is an odd prime, y > 1, k0, n is an integer greater than or equal to 4, (n,3h)=1 where h is the class number of the field Q(p), then the equation x2+p2k+1=4yn has exactly five families of solution in the positive integers x, y. It is further proved that when n=3 and p...