J. Grau

activity

20102025

most citedOn the diameter of the commuting graph of the full matrix ring over the real numbers

9 citations · 36 across the 31 of their papers we have counts for

collaborators

Showing 2011Show all

5 papers · 1 filter

math.NT2011

Corrigendum to "Cullen numbers with the Lehmer Property"

José María Grau, Florian Luca

In this note, we correct an oversight from the paper mentioned in the title.

math.NT2011

Cullen Numbers with the Lehmer Property

Jose Maria Grau, Florian Luca

Here, we show that there is no positive integer $n$ such that the $n$ th Cullen number $C_{n} = n 2^{n} + 1$ has the property that it is composite but $ϕ (C_{n}) ∣ C_{n} - 1$ .

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…

math.NT2011

On a variant of Giuga numbers

Jose Maria Grau, Florian Luca, Antonio M. Oller-Marcen

In this paper, we characterize the odd positive integers $n$ satisfying the congruence $\sum_{j = 1}^{n - 1} j^{\frac{n - 1}{2}} \equiv 0 (mod n)$ . We show that the set of such positive…

math.NT2011★ 5 cited

Giuga Numbers and the arithmetic derivative

José María Grau, Antonio M. Oller-Marcén

We characterize Giuga Numbers as solutions to the equation $n^{'} = an + 1$ , with $a \in N$ and $n^{'}$ being the arithmetic derivative. Although this fact does not refute Lava's co…