Displaying similar documents to “Two Diophantine cubics”

Diophantine equation q n - 1 q - 1 = y for four prime divisors of y - 1

Zdeněk Polický (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper the special diophantine equation q n - 1 q - 1 = y with integer coefficients is discussed and integer solutions are sought. This equation is solved completely just for four prime divisors of y - 1 .

On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II

D. Poulakis, P. G. Walsh (2006)

Colloquium Mathematicae

Similarity:

Let p denote a prime number. P. Samuel recently solved the problem of determining all squares in the linear recurrence sequence {Tₙ}, where Tₙ and Uₙ satisfy Tₙ² - pUₙ² = 1. Samuel left open the problem of determining all squares in the sequence {Uₙ}. This problem was recently solved by the authors. In the present paper, we extend our previous joint work by completely solving the equation Uₙ = bx², where b is a fixed positive squarefree integer. This result also extends previous work...

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

Amir Khosravi, Behrooz Khosravi (2003)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.