given a positive integer $N$ greater than $3$, is there a smart or algorithmic way to find the smallest number $M$ for which the remainder of $N/M$ equals $3$? one obvious answer is always $N-3$, but this is rarely the smallest one.
2026-04-14 18:52:12.1776192732
find smallest number $M$ for which the remainder of $N/M$ is equal to $3$
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The desired $M$ is the smallest divisor of $N-3$ that is greater than $3$. If you have the prime factorization of $N-3$, this is easy to find; if not, I don't know an efficient procedure. (There is of course a simple procedure: just test possible divisors starting with $4$.)