Note on a Fermat-type diophantine equation Original Research Article

Let p>5 be a prime number and ζ a pth root of unity. Let c be an integer divisible only by primes of the form kp−1, (k,p)=1. Let Cp(i) be the eigenspace of the p-Sylow subgroup of ideal class group C of Q(ζ) corresponding to ωi, ω being the Teichmuller character. In this article we extend the main theorem in Sitaraman (J. Number Theory 80 (2000) 174) and get the following: For any fixed odd positive integer n