Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   examine generalisations of the following problem posed by Laczkovich: Given an nxm rectangle with n and m integers, it can be written as a disjoint union of squares; what is the smallest number of squares that can be used? He also asked the corresponding higher dimensional analogue. For the two dimensional case Kenyon proved a tight logarithmic bound but left open the higher dimensional case. Using completely different methods  prove good upper and lor bounds for this case as ll as some other variants.
['Mark Walters']
I am writing a research paper on a idea Rectangles as sums of squares
[{"from": "human", "value": "I am writing a research paper on a idea Rectangles as sums of squares"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   examine generalisations of the following problem posed by Laczkovich: Given an nxm rectangle with n and m integers, it can be written as a disjoint union of squares; what is the smallest number of squares that can be used? He also asked the corresponding higher dimensional analogue. For the two dimensional case Kenyon proved a tight logarithmic bound but left open the higher dimensional case. Using completely different methods  prove good upper and lor bounds for this case as ll as some other variants."}]