For dense enough subsets A,B of (N,2N], there exist a in A and b in B with ab = P_k^2 + O(P_k^{1-delta}) for an almost-prime P_k.
Bordell` es, A note on a multiplicative hybrid problem, Acta Arith
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On a multiplicative hybrid problem over almost-primes
For dense enough subsets A,B of (N,2N], there exist a in A and b in B with ab = P_k^2 + O(P_k^{1-delta}) for an almost-prime P_k.