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First, we have to assume that all perfect numbers N can be written as
for positive integer k.
Let m, m+1, ..., (m+2^n)-2 be the (2^n) - 1 consecutive numbers, in which their sum is
We want to show that all perfect numbers N can be expressed in this form. However, if we set m = 1 the solution becomes trivial.
Alternatively, we can let
in which N becomes the sum of the first (2^k) - 1 integers.