Geodesic
On Product Decompositions
Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 739-746

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Borsuk has asked whether there exists for each compact metric absolute neighbourhood retract X an integer l (depending only on X) with the property that if X is homotopy equivalent to a cartesian product of more than l spaces than at least one of these spaces is contractible. The answer to this question is still not known. The following theorem has been proved by Ganea and Hilton [Theorem 1.3 of [1]]. 
Varadarajan, K. On Product Decompositions. Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 739-746. doi: 10.4153/CMB-1974-133-6
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     title = {On {Product} {Decompositions}},
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     doi = {10.4153/CMB-1974-133-6},
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