Hatice I Kübra Ayranci: Perfekta tal och Mersenne primtal

Abstract: Perfect numbers are positive integers that equal the sum of their proper divisors. The two smallest perfect numbers are 6 and 28. Mersenne primes are prime numbers of the form 2^p-1, where p is itself a prime number. The two smallest Mersenne primes are 3 and 7. In this work we show that there is a surprising bijection between Mersenne primes and even perfect numbers. It is not known if there exist any odd perfect numbers.