Ramanujan observed 1729 is the smallest positive # expressible as a sum of 2 cubes in 2 ways. What's the counterpart for _squares_?
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Replying to @stevenstrogatz
Hang on. What's wrong with 25 = 3^2 + 4^2 = 0^2 + 5^2?
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Replying to @MathPrinceps
The intended question is for sums of squares of _positive_ integers.
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Replying to @stevenstrogatz
The counterpart for squares: Smallest positive # expressible as a sum of 2 squares in 2 ways. Doesn't say non-zero squares.
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Replying to @MathPrinceps
were you concerned that Hardy did not write "...sum of two _positive_ cubes in two different ways"? (Of course he should have)
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Replying to @stevenstrogatz @MathPrinceps
Re squares, if we allow non-positive integers, 0^2+1^2=0^2+(-1)^2 would be a smaller positive sum than your example.
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Replying to @stevenstrogatz
Ramanujan's was more interesting, and, in a sense, more ingenious. This is a lovely exposition: http://bit.ly/1WIx4vH
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Replying to @stevenstrogatz @MathPrinceps
do we have an answer for "squares" ??
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Yes: If 0^2 is allowed, then 25. If not, then 50.
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