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??).

(In reply to re: computer solution by Charlie)

Right you are ... it was just a complete failure of a post. My program output wasn't nicely formatted, and while it had given additional solutions, they were all mixed up and I just lost them. After putting what I thought were the only solutions into my post, I made that comment based on the solutions I had seen.

I just deleted that part of my post, leaving my part A answer only. Next time I should probably do a little bit of double checking before I post. =)

Posted by Justin on 2010-08-02 16:34:03