Find all possible values of a composite positive integer N such that every divisor, D, of N (excluding N) satisfies:
N-20 ≤ D ≤ N-12

I'm assuming trivial and negative divisors are excluded, in accordance with convention:https://en.wikipedia.org/wiki/Divisor and http://mathworld.wolfram.com/Divisor.html. Otherwise, the puzzle just becomes a trick question about the definition of 'divisor.'

5*5=25, meets the puzzle's demands, as I understand it, since 25-20=5. This looks like an upper bound as far as prime candidates are concerned.

The only other candidate I can see is 3*7=21.

But in that case, I'm not really sure why this problem is D3, so I'm probably missing something.

Edited on January 18, 2016, 11:11 am

Posted by broll on 2016-01-18 10:44:24