3 research outputs found
Prime factors of of the same form
We parameterize solutions to the equality
when each is
prime. Our focus is on the special cases when , as this analysis
simplifies and extends bounds on the total number of prime factors of an odd
perfect number
On a theorem of Kanold on odd perfect numbers
We shall prove that if is an odd perfect number such that are distinct primes, and divides
for all , then divides , improving
an eighty-year old result of Kanold.Comment: 8 pages, the author's final version of the paper of the same title in
Indian J. Pure Appl. Math, which is available at
https://doi.org/10.1007/s13226-023-00530-