On the existence of a new family of Diophantine equations for $\bf Ω$
| dc.creator | Ord, Toby | |
| dc.creator | Kieu, Tien D. | |
| dc.date | 2003-01-24 | |
| dc.date | 2003-10-12 | |
| dc.date.accessioned | 2026-07-07T04:54:39Z | |
| dc.date.available | 2026-07-07T04:54:39Z | |
| dc.description | We show how to determine the $k$-th bit of Chaitin's algorithmically random real number $Ω$ by solving $k$ instances of the halting problem. From this we then reduce the problem of determining the $k$-th bit of $Ω$ to determining whether a certain Diophantine equation with two parameters, $k$ and $N$, has solutions for an odd or an even number of values of $N$. We also demonstrate two further examples of $Ω$ in number theory: an exponential Diophantine equation with a parameter $k$ which has an odd number of solutions iff the $k$-th bit of $Ω$ is 1, and a polynomial of positive integer variables and a parameter $k$ that takes on an odd number of positive values iff the $k$-th bit of $Ω$ is 1. | |
| dc.identifier | https://arxiv.org/abs/math/0301274 | |
| dc.identifier | http://arxiv.org/abs/math/0301274 | |
| dc.identifier | Fundamenta Informaticae 56 (2003) 273--284 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66341 | |
| dc.subject | Number Theory | |
| dc.subject | Computational Complexity | |
| dc.subject | Quantum Physics | |
| dc.title | On the existence of a new family of Diophantine equations for $\bf Ω$ | |
| dc.type | text |