On a Diophantine problem with two primes and s powers of two
The number of solutions of the congruence in the box is estimated from below in the best possible way, provided for all i,j either or or .
Given an integer , let be pairwise coprime integers , a family of nonempty proper subsets of with “enough” elements, and a function . Does there exist at least one prime such that divides for some , but it does not divide ? We answer this question in the positive when the are prime powers and and are subjected to certain restrictions.We use the result to prove that, if and is a set of three or more primes that contains all prime divisors of any number of the form for...