Thales12345
New member
- Joined
- Jul 3, 2021
- Messages
- 30
GIVEN: A strictly positive natural number n is "remarkable" if any strictly positive natural number less than or equal to n can be written as the sum of different divisors of n.
(Examples:
1 is remarkable
->1 = 1
2 is remarkable
->1 = 1
->2 = 2
4 is remarkable
->1 = 1
->2 = 2
->3 = 1 + 2
->4 = 4
6 is remarkable
->1 = 1
->2 = 2
->3 = 3
->4 = 1 + 3
->5 = 2 + 3
->6 = 6)
TO PROVE: 6^100 is remarkable
As I write out the sequence of numbers further, I quickly notice that every multiple of 6 belongs to the sequence. Is this sufficient as 'proof'?
(Examples:
1 is remarkable
->1 = 1
2 is remarkable
->1 = 1
->2 = 2
4 is remarkable
->1 = 1
->2 = 2
->3 = 1 + 2
->4 = 4
6 is remarkable
->1 = 1
->2 = 2
->3 = 3
->4 = 1 + 3
->5 = 2 + 3
->6 = 6)
TO PROVE: 6^100 is remarkable
As I write out the sequence of numbers further, I quickly notice that every multiple of 6 belongs to the sequence. Is this sufficient as 'proof'?