On a multiplicative hybrid problem over almost-primes
Abstract
Let N be a large enough natural number, A and B be subsets of N+1, ... , 2N. In this paper, we prove that there exists integers a, b with a belongs to A, b belongs to B such that ab=Pk2 + O(Pk1-c), where 0<c<1/2 and Pk denotes an almost-prime with at most k prime factors, counted with multiplicity.
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