Let $b>1$ be a fixed positive integer. We study the distribution of pseudoprimes to base $b$ in certain linear recurrence sequences. We prove, in effective form, that most terms of these sequences are not pseudoprimes to base $b$.

A consequence of the resolution of the Nielsen Realization Problem is that if $G$ is any finite topological group of automorphisms of a compact oriented surface $S$, then there exists a complex structure on $S$ so that the action of $G$ extends to a conformal action on $S$. We show that this complex structure is unique if and only if $G$ is a triangle group, and for all other groups, there are infinitely many such actions.

In this paper, it is shown that the Hilbert series of a Borel type ideal may be computed within a complexity which is polynomial in $D^n$ where $n+1$ is the number of unknowns and $D$ is the highest degree of a minimal generator of input (monomial) ideal.

In this paper we deal with the asymptotic behaviour of sample maxima of $L_p$-norm asymptotically spherical random vectors. If the distribution function of the associated random radius of such random vectors is in the Gumbel of the Weibull max-domain of attraction we show that the normalised sample maxima has asymptotic independent components converging in distribution to a random vector with unit Gumbel or Weibull components. When the associated random radius has distribution function in the Fréchet max-domain we show that the sample maxima has asymptotic dependent components.