Diophantine equation $\frac{q^n-1}{q-1}=y$ for four prime divisors of $y-1$

Zdeněk Polický

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Displaying similar documents to “Diophantine equation $\frac{q^{n} - 1}{q - 1} = y$ for four prime divisors of $y - 1$ ”

On Bumby’s equation ${(x^{2} - 2)}^{2} - 2 = 2 y^{2}$ : a solution via pythagorean triples

Ladislav Beran (1987)

Acta Universitatis Carolinae. Mathematica et Physica

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On the Diophantine equation $\frac{q^{n} - 1}{q - 1} = y$

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 $m \geq 2$ and $n \geq 3$ . 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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On Bumby’s equation ( x 2 - 2 ) 2 - 2 = 2 y 2 : a solution via pythagorean triples

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

Displaying similar documents to “Diophantine equation $\frac{q^{n} - 1}{q - 1} = y$ for four prime divisors of $y - 1$ ”

On Bumby’s equation ${(x^{2} - 2)}^{2} - 2 = 2 y^{2}$ : a solution via pythagorean triples

On the Diophantine equation $\frac{q^{n} - 1}{q - 1} = y$