Claims

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2003_01_01_skalba: Disproves the finiteness question as worded, with the number of blocks free: disjoint blocks of four consecutive positive integers have a square product infinitely often; refereed in 2003.

2005_01_01_ulas: Disproves the finiteness question by exhibiting infinitely many collections of n disjoint blocks of four consecutive integers whose product is a square, for n equal to four and every n at least six; refereed in 2005.

2007_01_01_bauer_bennett: Disproves the finiteness question with infinitely many collections of n disjoint blocks of four consecutive integers with square product for every n at least three, completing the cases Ulas left; refereed in 2007.

2012_03_01_bennett_van_luijk: Disproves the finiteness question with infinitely many collections of r disjoint blocks of five consecutive integers with square product for every r at least five; refereed in 2012.

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