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A note on ( a , b ) -Fibonacci sequences and specially multiplicative arithmetic functions

Emil Daniel Schwab, Gabriela Schwab (2024)

Mathematica Bohemica

A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely ( a , b ) -Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.

A quantitative primitive divisor result for points on elliptic curves

Patrick Ingram (2009)

Journal de Théorie des Nombres de Bordeaux

Let E / K be an elliptic curve defined over a number field, and let P ∈ E ( K ) be a point of infinite order. It is natural to ask how many integers n ≥ 1 fail to occur as the order of P modulo a prime of K . For K = ℚ , E a quadratic twist of y 2 = x 3 - x , and P ∈ E ( ℚ ) as above, we show that there is at most one such n ≥ 3 .

A search for Tribonacci-Wieferich primes

Jiří Klaška (2008)

Acta Mathematica Universitatis Ostraviensis

Such problems as the search for Wieferich primes or Wall-Sun-Sun primes are intensively studied and often discused at present. This paper is devoted to a similar problem related to the Tribonacci numbers.

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