$n$ is an 18-digit number, while $n/5$, $(n-1)/2$, $(n-2)/3$, $(n-3)/4$ are all primes. Find $n$.
Is there a theorem that can solve this kind of problem?
For example, The Chinese Remainder Theorem could solve issues that if one knows the remainders of the Euclidean division of an integer $n$ by several integers, then one can determine uniquely the remainder of the division of $n$ by the product of these integers, under the condition that the divisors are pairwise coprime.
However, this question is one step further, constraints are not only on the remainder but also on quotients.
So, are there related theorems, or such kind of questions are to be solved by brute force?