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

Amir Khosravi; Behrooz Khosravi

Displaying similar documents to “On the Diophantine equation $\frac{q^{n} - 1}{q - 1} = y$ ”

The method of infinite ascent applied on $A^{4} \pm n B^{3} = C^{2}$

Susil Kumar Jena (2013)

Czechoslovak Mathematical Journal

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Each of the Diophantine equations $A^{4} \pm n B^{3} = C^{2}$ has an infinite number of integral solutions $(A, B, C)$ for any positive integer $n$ . In this paper, we will show how the method of infinite ascent could be applied to generate these solutions. We will investigate the conditions when $A$ , $B$ and $C$ are pair-wise co-prime. As a side result of this investigation, we will show a method of generating an infinite number of co-prime integral solutions $(A, B, C)$ of the Diophantine equation $a A^{3} + c B^{3} = C^{2}$ for any co-prime integer pair $(a, c)$ . ...

On the Diophantine equation $x^{2} + 7 = y^{m}$

Samir Siksek, John E. Cremona (2003)

Acta Arithmetica

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A ternary Diophantine inequality over primes

Roger Baker, Andreas Weingartner (2014)

Acta Arithmetica

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Let 1 < c < 10/9. For large real numbers R > 0, and a small constant η > 0, the inequality $| p ₁^{c} + p ₂^{c} + p ₃^{c} - R | < R^{- η}$ holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].

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

Zdeněk Polický (2005)

Commentationes Mathematicae Universitatis Carolinae

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

On a ternary Diophantine problem with mixed powers of primes

Alessandro Languasco, Alessandro Zaccagnini (2013)

Acta Arithmetica

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Let 1 < k < 33/29. We prove that if λ₁, λ₂ and λ₃ are non-zero real numbers, not all of the same sign and such that λ₁/λ₂ is irrational, and ϖ is any real number, then for any ε > 0 the inequality $| λ ₁ p ₁ + λ ₂ p ² ₂ + λ ₃ p ₃^{k} + ϖ | \leq {(m a x_{j} p_{j})}^{- (33 - 29 k) / (72 k) + ε}$ has infinitely many solutions in prime variables p₁, p₂, p₃.

Displaying similar documents to “On the Diophantine equation q n - 1 q - 1 = y ”

The method of infinite ascent applied on A 4 ± n B 3 = C 2

On the Diophantine equation x 2 + 7 = y m

A ternary Diophantine inequality over primes

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

On a ternary Diophantine problem with mixed powers of primes

Displaying similar documents to “On the Diophantine equation $\frac{q^{n} - 1}{q - 1} = y$ ”

The method of infinite ascent applied on $A^{4} \pm n B^{3} = C^{2}$

On the Diophantine equation $x^{2} + 7 = y^{m}$

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