Let \(N\) be a Perfect Number (a positive integer that is equal to the sum of its proper positive divisors), like \(6\), or \(28\). It seems that all known perfect numbers are the sum of a series of consecutive positive integers starting with \(1\), that is, it seems that any perfect number is a triangular number. For example:
Prove that any even perfect number is triangular.
Note: It is not known whether there are any odd perfect numbers.