Claims

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1997_01_01_erdos_rosenfeld: Erdős and Rosenfeld prove that any number of integers can share two factor differences and print two triples sharing four, which settles k = 2 and k = 3.

1999_09_01_jimenez_urroz: Jiménez-Urroz proves that for every k there are k positive integers whose factor difference sets share at least three values, which settles k = 3.

2019_05_28_bremner: Bremner proves that there are infinitely many sets of four integers whose factor difference sets share four values, which settles k = 4.

2026_09_23_sanexxxx777: A Lean proof merged into formal-conjectures proves the k = 4 case with four integers whose factor difference sets share four values; this corpus has not built it.

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