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Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.

 May 11, 2020
 #1
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There isn't an actual strategic way I know of. For 1, I would have x = 0, y = 0, and z = 1, or x = 1, y = 0, z = 0, etc., for 2 I would have two of the three variables be 1, and so on. Like I said before, there isn't exactly a strategic way, and you might run into some radicals that aren't integers, like with four.

 May 11, 2020
 #2
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This is a conjecture in "advanced math" and can't be a school problem posed by your math teacher! As it happens, mathematicians have found solutions for all numbers from 1 to 100 with the possible exceptions of 33 and 42. I believe that recently even those two were solved. See this page for your own curiosity:

 

http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math04/matb0100.htm

 May 11, 2020

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