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Unsolved maths: Perfect Numbers

February 28, 2012

A perfect number is one where the proper factors of that number, add up to that number.
Eg 6 is perfect since:
1 + 2 + 3 = 6

Now, for any n,
2^n * [2^(n+1) – 1]
Is perfect if the part in square brackets is prime.
This is fairly cool.

What’s even more cool is that nobody knows whether there are any odd perfect numbers or not. Nobody can find one and nobody has shown that there definitely aren’t any either.

Such simple questions like ‘are there odd perfect numbers’ that can’t be answered yet is part of what makes me think that maths is amazing.

It is also a good counter example to students’ frequent feeling that maths is something that has ‘been done’ and they just have to learn.


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