Displaying similar documents to “Diophantine equation q n - 1 q - 1 = y for four prime divisors of y - 1 ”

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

Amir Khosravi, Behrooz Khosravi (2003)

Commentationes Mathematicae Universitatis Carolinae

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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.

On pseudoprimes having special forms and a solution of K. Szymiczek’s problem

Andrzej Rotkiewicz (2005)

Acta Mathematica Universitatis Ostraviensis

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We use the properties of p -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.