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 Ramanujan enforced. (Posted on 2010-08-02)
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??).

 See The Solution Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 solutions | Comment 4 of 5 |
Part A:
87539319 = 1673 + 4363 = 2283 + 4233 = 2553 + 4143
119824488 =  113 + 4933 =  903 + 4923 = 3463 + 4283
143604279 = 1113 + 5223 = 3593 + 4603 = 4083 + 4233
175959000 =  703 + 5603 = 1983 + 5523 = 3153 + 5253
327763000 = 3003 + 6703 = 3393 + 6613 = 5103 + 5803
...

Part B:
999 = 103 + -13 = 123 + -93
728 =  93 + -13 = 123 + -103
721 =  93 + -23 = 163 + -153

 Posted by Dej Mar on 2010-08-02 16:16:37

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