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 2013 · math.NTShow all

3 papers · 2 filters

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★ 5 cited

On the congruence $1^{m} + 2^{m} + \dots + m^{m} \equiv n (mod m)$ with $n ∣ m$

José María Grau, Antonio M. Oller-Marcén, Jonathan Sondow

We show that if the congruence above holds and $n ∣ m$ , then the quotient $Q := m / n$ satisfies $\sum_{p ∣ Q} \frac{Q}{p} + 1 \equiv 0 (mod Q)$ , where $p$ is prime. The only known s…

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…

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

On the congruence 1m+2m+⋯+mm≡n(modm) with n∣m

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

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

On the congruence $1^{m} + 2^{m} + \dots + m^{m} \equiv n (mod m)$ with $n ∣ m$

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