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Ramanujan enforced. (Posted on 2010-08-02) Difficulty: 4 of 5
1,729 is the least integer which equals the sum of two positive cubes in two different ways (see "taxicab number" on the web):
1,729 = 12^3+1^3 and 1,729 = 10^3+9^3.

a) Find an integer which equals the sum of two positive cubes in THREE different ways.
There is more than one solution.

b) Erasing the word "positive" in the 1st statement allows a lesser positive integer(s??) number(s??) to be presented as a sum of two cubes in two different ways.
Find it (them??).

No Solution Yet Submitted by Ady TZIDON    
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computer solution | Comment 1 of 5
Part A: The smallest integer that my program found was 87,539,319 (confirmed by the Taxicab number Wiki article)

Edited on August 2, 2010, 4:28 pm
  Posted by Justin on 2010-08-02 15:18:11

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