Body:↵
I am solving this problem:[problem:1474B]↵
↵
We need to find the smallest integer a such that:↵
↵
a has at least 4 divisors↵
the difference between any two divisors of a is at least d↵
↵
My idea is to construct a as:↵
↵
a = p⋅q↵
↵
where:↵
↵
p is the smallest prime such that p≥d+1↵
q is the smallest prime such that q≥p+d↵
↵
Then I output a=p⋅q.↵
[submission:373450651]↵
↵
This works for all samples I tested, but I am not fully sure about correctness for all d.↵
Can someone confirm if this construction is always optimal, or provide a counterexample if it fails?
I am solving this problem:[problem:1474B]↵
↵
We need to find the smallest integer a such that:↵
↵
a has at least 4 divisors↵
the difference between any two divisors of a is at least d↵
↵
My idea is to construct a as:↵
↵
a = p⋅q↵
↵
where:↵
↵
p is the smallest prime such that p≥d+1↵
q is the smallest prime such that q≥p+d↵
↵
Then I output a=p⋅q.↵
[submission:373450651]↵
↵
This works for all samples I tested, but I am not fully sure about correctness for all d.↵
Can someone confirm if this construction is always optimal, or provide a counterexample if it fails?
