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On the Diophantine equation q n - 1 q - 1 = y

Amir Khosravi;  Behrooz Khosravi — 2003

Commentationes Mathematicae Universitatis Carolinae

There exist many results about the Diophantine equation ( q n - 1 ) / ( q - 1 ) = y m , where m ≥ 2 and n ≥ 3 . In this paper, we suppose that m = 1 , n is an odd integer and q a power of a prime number. Also let y be an integer such that the number of prime divisors of y - 1 is less than or equal to 3 . Then we solve completely the Diophantine equation ( q n - 1 ) / ( q - 1 ) = y for infinitely many values of y . This result finds frequent applications in the theory of finite groups.

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