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n^n + 1 is a perfect number

Source: IMAR 2016 p4

September 27, 2018

number theoryperfect numberPerfect Numbers

Problem Statement

A positive integer

m

is perfect if the sum of all its positive divisors,

1

and

m

inclusive, is equal to

2m

. Determine the positive integers

n

such that

n^n + 1

is a perfect number.