a positive integer $n$ is called a clt number if every group of order $n$ satisfies the converse of lagrange's theorem. in this note, we find all clt and supersolvable numbers up to $1000$. we also formulate some questions about the distribution of these numbers.

a positive integer $n$ is called a clt number if every group of order $n$ satisfies the converse of lagrange's theorem‎. ‎in this note‎, ‎we find all clt and supersolvable numbers up to $1000$‎. ‎we also formulate some questions about the distribution of these numbers‎.

The proposed European system for electronic identities, authentication, and trust services (eIDAS) enables remote authentication of an identity card (and selected data of the card) to an eID service. The core system has already been running on the German identity card since 2010. We analyze an extension proposed by Bundesdruckerei that enables the protocol to authenticate further transaction da...

Quantum mechanical ro-vibrational calculations are presented for the ArHC1 van der Waals complex using Hutson and Howard's empirical M5 potential. Analysis of the nodal structures, second differences and overlapping avoided crossings suggests that the higher bound states of ArHC1 are chaotic. This chaos is made evident by perturbing the angular part of the kinetic energy term, e.g. by isotopic ...

The implementer of an empirical test for random number generators is faced with some difficult problems, especially if the test is based on a statistic which is known only approximately: How can the test be tested? How can the approximation be improved? When is it good enough? A number of principles can be applied to these problems. These principles are illustrated using implementations of the ...