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Unformatted text preview: he had taken to the hospital was not an interesting number. Ramanujan disagreed, saying that it is the smallest positive integer that can be written as the sum of two cubes in two different ways. (i) Prove that Ramanujan’s statement is true. Solution. First, 1729 is the sum of two cubes in two different ways: 1729 = 1 3 + 12 3 ; 1927 = 9 3 + 10 3 . Second, no smaller number n has this property. If n = a 3 + b 3 , then a , b ≤ 12. It is now a matter of checking all pairs a 3 + b 3 for such a and b ....
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.
 Fall '11
 KeithCornell

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