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MathematicalPhysicist

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Assume there exists an odd perfect number ##2n+1##, then by definition ##2n = \sum_{m\ne 1, 2n+1, m|(2n+1)}m##.

So, since m is odd (since 2n+1 is odd and it divides it), if you can prove that the sum has an odd number of terms then obviously we get a contradiction.

What is known of the number of divisors of an odd number?