Patrick Brown

activity

20102016

most citedA Partial Proof of a Conjecture of Dris

5 citations · 5 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2016★ 5 cited

A Partial Proof of a Conjecture of Dris

Patrick Brown

Euler showed that if an odd perfect number $N$ exists, it must consist of two parts $N = q^{k} n^{2}$ , with $q$ prime, $q \equiv k \equiv 1 (mod 4)$ , and gcd $(q, n) = 1$ . Dris conjectured…

math.NT2015

More on the Nonexistence of Odd Perfect Numbers of a Certain Form

Patrick Brown

Euler showed that if an odd perfect number exists, it must be of the form $N = p^{α} q_{1}^{2 β_{1}}$ $\dots$ $q_{k}^{2 β_{k}}$ , where $p, q_{1}, \dots, q_{k}$ are distinct odd primes,…

math.CO2010

The Rees product of posets

Patricia Muldoon Brown, Margaret A. Readdy

We determine how the flag f-vector of any graded poset changes under the Rees product with the chain, and more generally, any t-ary tree. As a corollary, the Möbius function of the…