On a problem of Erdös related to common factor differences
Let [Formula: see text] be a positive integer. The factor-difference set [Formula: see text] of [Formula: see text] is the set of absolute values [Formula: see text] of the differences between the factors of any factorization of [Formula: see text] as a product of two integers. Erdős and Rosenfeld [The factor–difference set of integers, Acta Arith. 79(4) (1997) 353–359] ask whether for every positive integer [Formula: see text] there exist integers [Formula: see text] such that [Formula: see text], and prove this is true when [Formula: see text]. Urroz [A note on a conjecture of Erdős and Rosenfeld, J. Number Theory 78(1) (1999) 140–143] shows the result true for [Formula: see text]. The ideas of this paper can be extended, and here, we show the result true for [Formula: see text] by proving there are infinitely many sets of four integers with four common factor differences.