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[7] [8] [9] It is widely believed, [10] but not proven, that no odd perfect numbers exist; numerous restrictive conditions have been proven, [10] including a lower bound of 10 1500. [11] The following is a list of all 52 currently known (as of January 2025) Mersenne primes and corresponding perfect numbers, along with their exponents p.
Sophistication of books is the practice of making a book complete by replacing missing leaves with leaves from another copy. In some cases this is done with the intent to deceive or mislead, modifying and offering books for sale in an attempt to sell them for a higher value.
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
In terms of universal properties, the perfect closure of a ring A of characteristic p is a perfect ring A p of characteristic p together with a ring homomorphism u : A → A p such that for any other perfect ring B of characteristic p with a homomorphism v : A → B there is a unique homomorphism f : A p → B such that v factors through u (i.e ...
How to Be Perfect: The Correct Answer to Every Moral Question is a 2022 non-fiction book by American television producer and author Michael Schur. The book provides an introduction to many philosophical arguments on the concept of ethics , told largely in layman's terms and in a humorous tone.
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