J. Grau

most citedGeneralizing Giuga's conjecture

5 citations · 10 across the 4 of their papers we have counts for

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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…

math.NT2010

A primality test for $K p^{n} + 1$ numbers

José María Grau, Antonio M. Oller-Marcén

In this paper we generalize the classical Proth's theorem for integers of the form $N = K p^{n} + 1$ . For these families, we present a primality test whose computational complexity is $\w…

Cullen Numbers with the Lehmer Property

Generalizing Giuga's conjecture

On a variant of Giuga numbers

Giuga Numbers and the arithmetic derivative

A primality test for Kpn+1 numbers

A primality test for $K p^{n} + 1$ numbers