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Given several completely qj-additive integer functions with pairwise prime qj's, we consider their joint behavior modulo some integer vector. Under several natural conditions, it is possible to show that this behavior displays some “independence” properties with respect to the various moduli. In this paper we deal with this phenomenon along arithmetic sequences, as well as on short intervals.
Consider the multiplicities ep1(n),ep2(n),…,epk(n) in which the primes p1,p2,…,pk appear in the factorization of n!. We show that these multiplicities are jointly uniformly distributed modulo (m1,m2,…,mk) for any fixed integers m1,m2,…,mk, thus improving a result of Luca and Stănică [F. Luca, P. Stănică, On the prime power factorization of n!, J. Number Theory 102 (2003) 298–305]. To prove the theorem,...
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