Are there infinitely many even perfect numbers?
Take a positive whole number, like, for example, 6. Write down all of its positive divisors except itself. For example, 1 divides 6, 2 divides 6 and 3 divides 6. Add up all these divisors. Here we get 1+2+3=6. Remarkably, we got our original number back. That was not a magic trick, in fact it doesn't usually work if you don't start with the right number, but 6 was a very special number. Any positive whole number which is the sum of all of its positive divisors, not including itself, is called a perfect number. Only about 50 perfect numbers have been discovered. Are there any more? Are there 100 of them? Are there infinitely many? Can you prove it? Or can you disprove it?
The image shows the first 6 perfect numbers. Source: Wikipedia contributors. "List of perfect numbers". Wikipedia, The Free Encyclopedia. 15 Dec. 2009. Retrieved 21 Mar. 2010.