16 Citations
A note on diophantine representations
- Mathematics
- 1993
In 1900 David Hilbert asked for an algorithm to decide whether a given diophantine equation is solvable or not and put this problem tenth in his famous list of 23. In 1970 it was proved that such an…
Prime Representing Polynomial
- MathematicsFormaliz. Math.
- 2021
Summary The main purpose of formalization is to prove that the set of prime numbers is diophantine, i.e., is representable by a polynomial formula. We formalize this problem, using the Mizar system…
A Diophantine representation of Wolstenholme's pseudoprimality
- MathematicsCILC
- 2015
It is shown that the upper bound for the number of variables in a prime-representing polynomial could be lowered to 8 if the converse of Wolstenholme's theorem (1862) holds, as conjectured by James P. Jones.
Exponential prefixed polynomial equations
- Mathematics
- 2013
A prefixed polynomial equation is an equation of the form $P(t_1,\ldots,t_n) = 0$, where $P$ is a polynomial whose variables $t_1,\ldots,t_n$ range over the natural numbers, preceded by quantifiers…
Gibt es primzahldefinierende Funktionen
- 2011
Die Untersuchung von Primzahlen wirft die Frage auf, ob es nicht einfach berechenbare Funktionen f(n) gibt, die fur alle naturlichen Zahlen n definiert sind und einige oder alle Primzahlen…
What can and cannot be done with Diophantine problems
- Mathematics
- 2011
This survey presents various theorems (obtained mainly by specialists in mathematical logic and computability theory) stating the impossibility of algorithms for solving certain Diophantine problems.…
The Little Book of Bigger Primes
- Mathematics, Philosophy
- 2004
How Many Prime Numbers Are There?.- How to Recognize Whether a Natural Number is a Prime.- Are There Functions Defining Prime Numbers?.- How Are the Prime Numbers Distributed?.- Which Special Kinds…
Od Fermatových prvočísel ke geometrii
- Physics
- 2002
V tomto clanku M. Křižek zkouma výskyt Fermatových cisel v geometrii. Nejprve ve zkratce vysvětluje, co to Fermatova cisla jsou a jaka jsou dnes znama. V dalsi kapitole ukazuje využiti Fermatových…