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Criteria for testing Wall's question

Jiří Klaška — 2008

Czechoslovak Mathematical Journal

In this paper we find certain equivalent formulations of Wall's question and derive two interesting criteria that can be used to resolve this question for particular primes.

Short remark on Fibonacci-Wieferich primes

Jiří Klaška — 2007

Acta Mathematica Universitatis Ostraviensis

This paper has been inspired by the endeavour of a large number of mathematicians to discover a Fibonacci-Wieferich prime. An exhaustive computer search has not been successful up to the present even though there exists a conjecture that there are infinitely many such primes. This conjecture is based on the assumption that the probability that a prime p is Fibonacci-Wieferich is equal to 1 / p . According to our computational results and some theoretical consideratons, another form of probability can...

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.

Transitivity and partial order

Jiří Klaška — 1997

Mathematica Bohemica

In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary n -element set up to n = 14 .

Tribonacci modulo p t

Jiří Klaška — 2008

Mathematica Bohemica

Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus p and by its powers p t , which were deduced by M. E. Waddill. In this paper we derive similar results for the case of a Tribonacci sequence that starts with an arbitrary triple of integers.

Tribonacci modulo 2 t and 11 t

Jiří Klaška — 2008

Mathematica Bohemica

Our previous research was devoted to the problem of determining the primitive periods of the sequences ( G n mod p t ) n = 1 ∞ where ( G n ) n = 1 ∞ is a Tribonacci sequence defined by an arbitrary triple of integers. The solution to this problem was found for the case of powers of an arbitrary prime p ≠ 2 , 11 . In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes p = 2 , 11 .

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