scholarly journals The Form of Even Perfect Numbers-- an Independent Derivation

2018 ◽  
Author(s):  
Nirmalya Basu
Keyword(s):  
Perfect Numbers ◽  
Independent Derivation

Here, I present my own, independently pursued derivation of the general form of even perfect numbers.

Perfect Numbers

1910 ◽  
Vol 17 (8-9) ◽  
pp. 165-168
Author(s):  
T. M. Putnam
Keyword(s):  
Perfect Numbers

65.1 Even Perfect Numbers

1981 ◽  
Vol 65 (431) ◽  
pp. 28 ◽  
Author(s):  
Graeme L. Cohen
Keyword(s):  
Perfect Numbers

A lower bound for \tau(n) of any k-perfect numbers

2015 ◽  
Vol 4 ◽  
pp. 99-103
Author(s):  
Keneth Adrian P. Dagal
Keyword(s):  
Lower Bound ◽  
Perfect Numbers

Pseudoperfect numbers with no small prime divisors

2009 ◽  
Vol 93 (528) ◽  
pp. 404-409
Author(s):  
Peter Shiu
Keyword(s):  
Difficult Problem ◽  
Prime Divisors ◽  
Perfect Number ◽  
Perfect Numbers ◽  
Mersenne Primes ◽  
Mersenne Prime

A perfect number is a number which is the sum of all its divisors except itself, the smallest such number being 6. By results due to Euclid and Euler, all the even perfect numbers are of the form 2P-1(2p - 1) where p and 2p - 1 are primes; the latter one is called a Mersenne prime. Whether there are infinitely many Mersenne primes is a notoriously difficult problem, as is the problem of whether there is an odd perfect number.

scholarly journals Revisiting some old results on odd perfect numbers

2018 ◽  
Vol 24 (4) ◽  
pp. 18-25
Author(s):  
Jose Arnaldo Bebita Dris ◽  
◽  
Doli-Jane Uvales Tejada ◽  
Keyword(s):  
Perfect Numbers

scholarly journals Some modular considerations regarding odd perfect numbers – Part II

2020 ◽  
Vol 26 (3) ◽  
pp. 8-24
Author(s):  
Jose Arnaldo Bebita Dris ◽  
◽  
Immanuel Tobias San Diego ◽  
Keyword(s):  
Perfect Numbers
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