We prove an euclid-like theorem for near-perfect numbers and obtain of 2012, donavan johnson found the first odd near-perfect number. In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the. A perfect number is a positive integer that equals the sum of its proper divisors, that is, positive divisors excluding the number itself for example,.
Euclid discovered that the first four perfect numbers are generated by the for- mula 2n^1(2n − 1) he also noticed that 2n − 1 is a prime number for every instance. The talk was titled some recent results on odd perfect numbers a number is called perfect if it is the sum of its positive factors other than. Six is a perfect number as it is the sum of its factors can you find any other perfect numbers. Frequently asked questions what are perfect, adundant, and deficient numbers the divisors of a natural number, excluding the number itself, are called the. This study is on odd perfect numbers, and the conditions which limit their existence correspondence between even perfect numbers and mersenne primes (a.
It is not known whether there are any odd perfect numbers, or whether there are infinitely many even perfect numbers the existence of infinitely many even. 1 introduction a positive number n 0 is called perfect if it is equal to the sum σ(n ) − n of its proper divisors some classical papers on perfect numbers were. Recall that a prefect number is equal to the sum of its divisors if you include 1 as a we show that if n is an even perfect number than there exists k such that n is . We recall that perfect numbers (sequence a000396 of sloane's while it is still not known whether there exist any odd perfect numbers, euler  proved.
Looking for the perfect date numerically today is the only day of the year where both the month (6) and the date (28) are different perfect numbers june 6 is the. We prove that a relation between even perfect numbers and mersenne prime numbers proved by euclid and euler definitions, open problems. Interviewer: there's a unicorn standing there but these two explorers are only interested in the number too funny cartoonist: what there's a unicorn.
6 : the divisors of 6 are 1,2,3 & 6 to show that this is a perfect number we could all the divisors except the number itself 1+2+3 = 6 28 1 + 2 + 4 + 7 + 14 =28. The study of perfect numbers is an area of the theory of numbers which dates back to antiquity a positive integer n is a perfect number if and only if the sum of its. A perfect number is a number that is equal to the sum of all its factors other than itself.