On: "Embarrassing" open problems in maths

[splat]

I'm reminded of two other "embarrassing" open problems.

A perfect number is a number whose divisors sum to return the original number. Thus, 6 is a perfect number since 1 + 2 + 3 = 6. 28 is also a perfect number since 1 + 2 + 4 + 7 + 14 = 28. But 8 is not a perfect number since 1 + 2 + 4 = 7.

1. Are there an infinite number of perfect numbers?

2. Are there any odd perfect numbers?

[yequalsx → splat]

A slight nitpick. Your definition should be a number whose proper divisors sum to the original number. Or it should be whose divisors sum to twice the original number.

[splat → yequalsx]

Point taken, good catch.