Paolo Starni

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math.NT2017

Some Extensions to Touchard's Theorem on Odd Perfect Numbers

Paolo Starni

The multiplicative structure of an odd perfect number $n$ , if any, is $n = π^{α} M^{2}$ , where $π$ is prime, $g cd (π, M) = 1$ and $π \equiv α \equiv 1 (mod 4)$ . An additive structure of $n$ , es…

math.NT2017

On Dris Conjecture about Odd Perfect Numbers

Paolo Starni

The Euler's form of odd perfect numbers, if any, is $n = π^{α} N^{2}$ , where $π$ is prime, $(π, N) = 1$ and $π \equiv α \equiv 1 (mod 4)$ . Dris conjecture states that $N > π^{α}$ . We find that $N…