P. Leonetti

activity

20122026

most citedOn the notions of upper and lower density

20 citations · 109 across the 55 of their papers we have counts for

collaborators

Showing 2013Show all

2 papers · 1 filter

math.NT2013★ 4 cited

A characterization of Sophie Germain primes

Paolo Leonetti

Let $n \geq 5$ be an odd integer. It is shown that ${1^{σ (1)}, \dots, n^{σ (n)}}$ is a complete residue system modulo $n$ for some permutation $σ$ of ${1, \dots, n}$ if and only if…

math.NT2013

On consecutive perfect powers with elementary methods

Paolo Leonetti

Catalan's conjecture claims that the Diophantine equation $x^{p} - y^{q} = 1$ admits the unique solution $3^{2} - 2^{3} = 1$ in integers $x, y, p, q \geq 2$ . The conjecture has been finally proved by…