In fact, a very noted professor in Berlin University developed

a series of properties of odd perfect numbers in his lectures
on the theory of numbers, and then followed these developments
with the statement that it is not known whether any such
numbers exist
In fact, a very noted professor in Berlin University developed
a series of properties of odd perfect numbers in his lectures
on the theory of numbers, and then followed these developments
with the statement that it is not known whether any such
numbers exist. This raises the interesting philosophical
question whether one can know things about what is not known to
exist; but the main interest from our present point of view
relates to the fact that the meaning of odd perfect number is
so very elementary that all can easily grasp it, and yet no one
has ever succeeded in proving either the existence or the
non-existence of such numbers.


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