548
: A Perfect Number with a Mysterious History Have you ever heard of perfect numbers? They are a very special type of number that has fascinated mathematicians for centuries. A perfect number is a positive integer that is equal to the sum of its proper divisors. For example, the first perfect number is 6, because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 =
6. The second perfect number is 28, because its proper divisors are 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 2
8. But what about the perfect number 548? It might not be as famous as 6 or 28, but it is a perfect number nonetheless. Its proper divisors are 1, 2, 4, 137, and 274, and 1 + 2 + 4 + 137 + 274 = 418, which is twice 54
8. Despite its mathematical significance, not much is known about the history of 548 as a perfect number. It was first mentioned in a manuscript written by the ancient Greek mathematician Nicomachus of Gerasa in the 2nd century AD. Nicomachus called it a "superabundant" number because its sum of divisors is greater than the number itself. Later, the 6th-century mathematician and philosopher Boethius wrote about perfect numbers in his De Institutione Arithmetica, and mentioned 548 specifically. He believed that 548 was a "felicitous" number, meaning it had a special significance or good fortune attached to it. Unfortunately, we may never know why Boethius thought 548 was so special, or whether Nicomachus or anyone else in ancient times shared his opinion. But one thing we do know is that perfect numbers continue to inspire wonder and curiosity in mathematicians and non-mathematicians alike. Who knows what else we might discover about them in the future?