Slightly less trivial case (?): If p is safe prime (A5385) then binomial (p, p - 2) is the product of two primes p and (p-1)/2 (semiprime A1358) .
Суббота, 7 января 2017, 5:53 +03:00 от Marc LeBrun <mlb@well.com>:
(I think Dan meant a “non-trivial” binomial. But you knew that.)
On Jan 6, 2017, at 5:10 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com > wrote:
Q = binomial(Q,1).
-- Gene
From: Dan Asimov < dasimov@earthlink.net > To: math-fun < math-fun@mailman.xmission.com > Sent: Friday, January 6, 2017 4:30 PM Subject: [math-fun] Detecting binomial coefficients
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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