Oct 16, 2018 · A perfect number is a number than can be expressed as a sum of its factors. For example, 28 = 1 + 2 + 4 + 7 + 14 Why is this property important? What is so perfect about perfect …

Applications of Fermat numbers: relation to constructible polygons But for perfect numbers the best I could find is: The earth was created in 6 days by God because 6 is perfect.

May 3, 2023 · As far as I can judge, when a number is perfect, then the sum of its divisors is the double of that number, so it can't have any other new prime factors (except for $2$, obviously).

A well known theorem by Euler states that every even perfect number is of the form $2^ {p-1} (2^p-1)$ where $2^p-1$ is prime (this is what is called a Mersenne prime).

Jan 28, 2023 · Surely, if the list of six ($6$) even $3$ -perfect numbers as given above is complete, and if there are no odd perfect numbers, then there are no other $3$ -perfect numbers.

Dec 24, 2017 · Historically, perfect numbers were hugely important for almost religious reasons e.g. by the pythagoreans. As for the duplicate answer and your complaint that those answers only mention …

The well known formula for perfect numbers is $$ P_n=2^{n-1}(2^{n}-1). $$ This formula is obtained by observing some patterns on the sum of the perfect number's divisors. Take for example $496$:...

Sep 4, 2017 · Odd perfect numbers do not exist. According to Euclid's formulae a perfect number is equal to $2^P(2^P-1$) where $2^P-1$ should be prime. Only $2$ is the even prime number and rest …

Nov 22, 2024 · 1 This conjecture is unknown to be true or false. It is known to be true if we restrict to only even perfect numbers. That is, the Euclid-Euler theorem states that all even perfect numbers …

Mar 17, 2016 · A perfect number is the sum of its (positive) divisors (excluding itself). I am wondering if a square could be a perfect number. If it is an odd square, then, excluding itself, it has an even num...