Denote $||x||=Min(x-[x],1-(x-[x]))$,it means the minimum distance between x and an integer.
Can we find a fast algorithm to get a natural number $n$ that satisfies $$||na||<p,||nb||<p,...$$ where $a,b,...$ are given irrational numbers,and $p$ is a positive real number.I know it exists infinite such $n$,but I wonder how to find them in a fast way.Thanks in advance!
A similar question was answered on MathOverflow.
It cited these notes which refer to this algorithm.