Differences of Harmonic Numbers and the $abc$-Conjecture

zbMath1439.11009arXiv1708.00620MaRDI QIDQ5223057

Natalia da Silva, Serban Raianu, Hector Salgado

Publication date: 5 July 2019

Full work available at URL: https://arxiv.org/abs/1708.00620

zbMATH Keywords

exponential Diophantine equation\(abc\)-conjectureharmonic numbersDirichlet's theoremmodular arithmeticGersonides' theorem

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Congruences; primitive roots; residue systems (11A07) Primes (11A41)

Cites Work

• On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
• On \(p^x-q^y=c\) and related three term exponential Diophantine equations with prime bases.
• Primes at a Glance
• Primary cyclotomic units and a proof of Catalans conjecture
• Small Two-Variable Exponential Diophantine Equations
• Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers
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