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 2014 · math.NTShow all

3 papers · 2 filters

math.NT2014

Counting invertible sums of squares modulo $n$ and a new generalization of Euler totient function

Catalina Calderon, Jose Maria Grau, A. Oller-Marcen +1

In this paper we introduce and study a family $Φ_{k}$ of arithmetic functions generalizing Euler's totient function. These functions are given by the number of solutions to the equat…

math.NT2014

A von Staudt-type formula for $z \in Z_{n} [i] \sum z^{k}$

Pedro Fortuny Ayuso, Jose Maria Grau, Antonio Oller-Marcen

In this paper we study the sum of powers in the Gaussian integers $G_{k} (n) := \sum_{a, b \in [1, n]} (a + bi)^{k}$ . We give an explicit formula for $G_{k} (n) (mod n)$ in t…

math.NT2014★ 1 cited

Fermat test with gaussian base and Gaussian pseudoprimes

Jose M. Grau, Manuel Rodríguez, A. Oller-Marcen +1

The structure of the group $(Z / n Z)^{⋆}$ and Fermat's little theorem are the basis for some of best-known primality testing algorithms. Many related concepts ari…

Counting invertible sums of squares modulo n and a new generalization of Euler totient function

A von Staudt-type formula for z∈Zn​[i]∑​zk

Fermat test with gaussian base and Gaussian pseudoprimes

Counting invertible sums of squares modulo $n$ and a new generalization of Euler totient function

A von Staudt-type formula for $z \in Z_{n} [i] \sum z^{k}$