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Further results on derived sequences.

Hare, Kevin G.; Yazdani, Soroosh — 2003

Journal of Integer Sequences [electronic only]

Multiplicative functions and $k$ -automatic sequences

Soroosh Yazdani — 2001

Journal de théorie des nombres de Bordeaux

A sequence is called $k$ -automatic if the $n$ ’th term in the sequence can be generated by a finite state machine, reading $n$ in base $k$ as input. We show that for many multiplicative functions, the sequence ${(f (n) mod v)}_{n \geq 1}$ is not $k$ -automatic. Among these multiplicative functions are $γ_{m} (n), σ_{m} (n), μ (n)$ et $φ (n)$ .

On the equation a³ + b³ⁿ = c²

Michael A. Bennett; Imin Chen; Sander R. Dahmen; Soroosh Yazdani — 2014

Acta Arithmetica

We study coprime integer solutions to the equation a³ + b³ⁿ = c² using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from ℚ-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.

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Currently displaying 1 – 3 of 3

Further results on derived sequences.

Multiplicative functions and $k$ -automatic sequences

On the equation a³ + b³ⁿ = c²

Advanced Search

Formula preview

Currently displaying 1 – 3 of 3

Further results on derived sequences.

Multiplicative functions and k -automatic sequences

On the equation a³ + b³ⁿ = c²

Multiplicative functions and $k$ -automatic sequences