A. M. Oller-Marcén

activity

20112022

most citedGiuga Numbers and the arithmetic derivative

5 citations · 13 across the 12 of their papers we have counts for

collaborators

12 papers

math.PR2022

A new method for computing asymptotic results in optimal stopping problems

L. Bayón, P. Fortuny, J. M. Grau +2

In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems…

math.NT2021

On $μ$ -Sondow Numbers

J. M. Grau, A. M. Oller-Marcén, D. Sadornil

Given an integer $μ$ , we study the numbers that satisfy the condition $\frac{μ}{n} + \sum_{p ∣ n} \frac{1}{p} \in N$ . This condition, which is reminiscent of the one s…

math.MG2019

Further generalizations of the parallelogram law

Antonio M. Oller-Marcén

In recent work by Alessandro Fonda, a generalization of the parallelogram law in any dimension $N \geq 2$ was given by considering the ratio of the quadratic mean of the measures of…

math.RA2017

Generalized Quaternion Rings over $Z / n Z$ for an odd $n$

J. M. Grau, C. Miguel, A. M. oller-Marcén

We consider a generalization of the quaternion ring $(\frac{a , b}{R})$ over a commutative unital ring $R$ that includes the case when $a$ and $b$ are not units of $R$ . In th…

math.NT2013

On the congruence $\sum_{j = 1}^{n - 1} j^{k (n - 1)} \equiv - 1 (mod n)$ . k-strong Giuga and k-Carmichael numbers

Antonio M. Oller-Marcén, José María Grau

In this work we consider the congruence $\sum_{j = 1}^{n - 1} j^{k (n - 1)} \equiv - 1 (mod n)$ for each $k \in N$ , thus extending Giuga's ideas for $k = 1$ . In particular, it is pr…

math.NT2013★ 1 cited

About the congruence $\sum_{k = 1}^{n} k^{f (n)} \equiv 0 (mod n)$

José María Grau, Antonio M. Oller-Marcén

In this paper we characterize, in terms of the prime divisors of $n$ , the pairs $(k, n)$ for which $n$ divides $\sum_{j = 1}^{n} j^{k}$ . As an application, we study the sets $\mathcal{M…

A new method for computing asymptotic results in optimal stopping problems

On μ-Sondow Numbers

Further generalizations of the parallelogram law

Generalized Quaternion Rings over Z/nZ for an odd n

On the congruence ∑j=1n−1​jk(n−1)≡−1(modn). k-strong Giuga and k-Carmichael numbers

About the congruence ∑k=1n​kf(n)≡0(mod n)

On $μ$ -Sondow Numbers

Generalized Quaternion Rings over $Z / n Z$ for an odd $n$

On the congruence $\sum_{j = 1}^{n - 1} j^{k (n - 1)} \equiv - 1 (mod n)$ . k-strong Giuga and k-Carmichael numbers

About the congruence $\sum_{k = 1}^{n} k^{f (n)} \equiv 0 (mod n)$