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

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7 papers · 1 filter

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.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…

math.NT2012★ 2 cited

A determinant of generalized Fibonacci numbers

Christian Krattenthaler, Antonio M. Oller-Marcén

We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the li…

math.NT2012

On the last digit and the last non-zero digit of $n^{n}$ in base $b$

José María Grau, Antonio M. Oller-Marcén

In this paper we study the sequences defined by the last and the last non-zero digits of $n^{n}$ in base $b$ . For the sequence given by the last digits of $n^{n}$ in base $b$ , we prove…

math.NT2011★ 5 cited

Generalizing Giuga's conjecture

José María Grau, Antonio M. Oller-Marcén

In 1950 G. Giuga studied the congruence $\sum_{j = 1}^{n - 1} j^{n - 1} \equiv - 1$ (mod $n$ ) and conjectured that it was only satisfied by prime numbers. In this work we generalize Giuga…

On μ-Sondow Numbers

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)

A determinant of generalized Fibonacci numbers

On the last digit and the last non-zero digit of nn in base b

Generalizing Giuga's conjecture

On $μ$ -Sondow Numbers

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

On the last digit and the last non-zero digit of $n^{n}$ in base $b$