On the greatest common divisor of \(u-1\) and \(v-1\) with \(u\) and \(v\) near \(\mathcal S\)-units

DOI10.1007/s00605-005-0303-6zbMath1107.11029OpenAlexW2131957643MaRDI QIDQ2581030

Florian Luca

Publication date: 10 January 2006

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-005-0303-6

zbMATH Keywords

Subspace Theorem\({\mathcal S}\)-units

Mathematics Subject Classification ID

Diophantine inequalities (11D75) Diophantine inequalities (11J25)

Related Items (7)

On the Multiplicative Group Generated by Two Primes in Z∕Q Z ⋮ Greatest common divisors of iterates of polynomials ⋮ Greatest common divisors for polynomials in almost units and applications to linear recurrence sequences ⋮ Greatest common divisors with moving targets and consequences for linear recurrence sequences ⋮ Greatest common divisors and Vojta's conjecture for blowups of algebraic tori ⋮ A note on the number of $S$-Diophantine quadruples ⋮ A cyclotomic generalization of the sequence \(\gcd(a^n-1, b^n-1)\)

Cites Work

• Diophantine approximation
• An upper bound for the g.c.d. of \(a^n-1\) and \(b^n -1\)
• A lower bound for the height of a rational function at \(S\)-unit points
• Logarithmic forms and group varieties.
• On the greatest prime factor of (𝑎𝑏+1)(𝑎𝑐+1)
• A quantitative lower bound for the greatest prime factor of (ab+1)(bc+1)(ca+1)

This page was built for publication: On the greatest common divisor of \(u-1\) and \(v-1\) with \(u\) and \(v\) near \(\mathcal S\)-units