Artin's conjecture on primes with prescribed primitive roots
A positive integer is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pólya numbers not exceeding a given number .
We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.