Majestic Perfect Numbers

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Definition: Perfect numbers are numbers that whose sum of its divisors (excluding itself) equals the number itself.

A neat example would be \(6\) :

Courtesy of Wikipedia

Courtesy of Wikipedia

The next perfect numbers are \(28, 496, 8128 \dots\). There are \(50\) known perfect numbers as of January \(2018\). Euclid proved a formation rule whereby \(\dfrac{q(q+1)}{2}\) is an even perfect number whenever \(q\) is a Mersenne Prime (of the form: \(2^n-1\)). The formula for an even perfect number is \(2^p-1(2^{p-1})\) where \(p\) and \(2^p-1\) are prime. It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist.

There are other variations of perfect numbers like Triperfect numbers, Quasiperfect numbers and many more! Sadly, the list of these variations have an ending and no ore of these have been found.

Note by Mohmmad Farhan
2 weeks, 2 days ago

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A little suggestion :

Please try to post any note completely and fully as much as possible. If it is a time taking process then write as much as you can and save that in Microsoft word. When the whole note is completed then paste the whole thing at once and post it.

Ram Mohith - 2 weeks, 1 day ago

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