hello mr Asimov, that's a good question, there are a number of ways, the factors of binomials always have a definite pattern, 1- first approach would be : by the size of Q, we can restrict the search to a given index. 2- we know also that the factors would be small in size, so the factoring of Q should be simple to do. 3- Once we have the list of factors, from 2 to m (m being the biggest prime), then we also know that the list from 2 to m has to be without holes in the list of primes. That does not solve it but at the least limits the number of cases to verify. Best regards, Simon Plouffe There Le 2017-01-07 à 01:30, Dan Asimov a écrit :
Suppose we are given the prime factorization of a rather large integer Q.
Is there a good algorithm for determining from this whether the number Q is a binomial coefficient?
I.e., whether there exist positive integers k < n such that
Q = n! / (k! (n-k)!)
.
—Dan
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