#math trivia for #September21: #264 is the sum of a square and a cube, and also of two squares and a cube. What are they?
— Burt Kaliski Jr. (@modulomathy) September 22, 2013
Answer: The square and cube are 256 = 162 and 8 = 23.
The two squares and cube are 4 = 22, 196 = 142, and 64 = 43; or 100 = 102, 100, and 64. (Or, trivially adapting the first answer, 0, 256 and 8.)
(For simplicity, I’ve assumed the cubes are positive; it would be interesting to see if allowing negative cubes — and thus potentially much larger squares — would yield further solutions.)
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