Determine the largest number of distinct positive integers you can have such that the difference between any two of them is prime, and this difference divides both of those numbers.
If there are at least 3 numbers and A, B and C are all odd, and in that order, A and C must differ by an even number greater than two, violating the rules. The same is true if all are even.
If one of the numbers is even, the two odd numbers must differ by 2, but 2 can't divide into any odd numbers.
All the numbers must be even, and the only difference allowed is in fact 2.
It seems the only such set would be the 2-member set [2,4].
|
|
Posted by Charlie
on 2024-03-06 09:15:31 |
possible solution
