Ramanujan observed 1729 is the smallest positive # expressible as a sum of 2 cubes in 2 ways. What's the counterpart for _squares_?
-
-
Replying to @stevenstrogatz
Hang on. What's wrong with 25 = 3^2 + 4^2 = 0^2 + 5^2?
1 reply 0 retweets 0 likes -
Replying to @MathPrinceps
The intended question is for sums of squares of _positive_ integers.
1 reply 0 retweets 1 like -
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.
2 replies 0 retweets 0 likes -
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)
1 reply 1 retweet 0 likes -
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.
#pedantic10 replies 1 retweet 0 likes
By the way, Euler's theory of numbers equal to a sum of two cubes in two ways was essentially similar to this.
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.