The Mysterious Math of Perfection — Quanta Magazine

My latest column for Quanta Magazine explores the mathematics of perfect numbers. Humans have been studying perfect numbers for thousands of years, but we still don’t know if an odd perfect number exists!

Euclid laid out the basics of perfect numbers over 2,000 years ago, and he knew that the first four perfect numbers were 6, 28, 496 and 8,128. Since then, many more perfect numbers have been discovered. But, curiously, they’re all even. No one has been able to find an odd perfect number, and after thousands of years of unsuccessful searching, it might be tempting to conclude that odd perfect numbers don’t exist. But mathematicians haven’t been able to prove that either. How is it that we can know so much about even perfect numbers without being able to answer the simplest question about an odd one? 

With some basic number theory and an assist from a famous formula from Algebra class, we can get pretty far into the world of perfect numbers. So read the full article here, and be sure to stick around for the exercises at the end!