Swammerdami
Squadron Leader
Let A be a finite set of positive integers, and N = |A| be the size of A.
We shall say that A is pleasant if for all x,y ∈ A
For example, suppose A = {2, 3, 4, 5, 6}. N = 5 and A is "almost" pleasant. Almost every x,y pair gives x / gcd(x,y) ≤ 5 but there is one exception: 6 / gcd(6,5) = 6/1 = 6. But 6 > 5.
Your mission is to find all (finite) pleasant sets! (If you're not required to prove your list complete, this is not overly difficult!)
If there's interest I will follow-up with hints and some background on the problem.
We shall say that A is pleasant if for all x,y ∈ A
x / gcd(x,y) ≤ N
(The gcd(x,y) -- greatest common divisor -- is the largest positive integer that divides both x and y.)For example, suppose A = {2, 3, 4, 5, 6}. N = 5 and A is "almost" pleasant. Almost every x,y pair gives x / gcd(x,y) ≤ 5 but there is one exception: 6 / gcd(6,5) = 6/1 = 6. But 6 > 5.
Your mission is to find all (finite) pleasant sets! (If you're not required to prove your list complete, this is not overly difficult!)
If there's interest I will follow-up with hints and some background on the problem.