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Eliot Ness meets Paul Erdős (Posted on 2015-01-23) Difficulty: 2 of 5
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself).

Prove:
i. There is no untouchable number that is one more than a prime.
ii. Except number 5, there is no untouchable number that is
three more than a prime.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution Comment 3 of 3 |
(In reply to re: Solution by Kenny M)

Jer's proof goes in the right direction.  We are asked to prove that p+1 IS NOT untouchable, so we have to produce a number whose proper divisors add to p+1.
  Posted by Steve Herman on 2015-01-26 08:51:40

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