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Timeline for Sums of cubes and more

Current License: CC BY-SA 2.5

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Nov 19, 2009 at 1:52 comment added Jason DeVito - on hiatus Every number can be written as [1 first power], "4 squares, or 9 cubes, or 19 fourth powers, etc.". As mentioned above, all sufficiently large numbers can be written as 16 fourth powers. Assuming that the 9 cubes is optimal in this sense (i.e., there are arbitrarily large numbers requiring all 9 cubes), we get an interesting sequence 1,4,9,16.... Is this just coincidence or can every sufficiently large natural number be expressed as k^2 kth powers? (I know NOTHING about this field, just found the question interesting...)
Oct 13, 2009 at 19:57 history answered David Zureick-Brown CC BY-SA 2.5