SOLUTION: A computer access-code number was designated in a special way. It was a 4-digit number. The nmber is the smallest integer that can be written as the sum of two positve cubes in t

Question 82690This question is from textbook Algebra 2 with Trigonometry
: A computer access-code number was designated in a special way. It was a 4-digit number. The nmber is the smallest integer that can be written as the sum of two positve cubes in two different ways, and the number is between 1000 and 2000. What is the code number? This question is from textbook Algebra 2 with Trigonometry

Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
Hi there,

I can't see a particularly simple way to solve this without using a computer to try out all the possibilities. There are however a few simplifications you can make. Firstly the biggest number you need to try is 12^3, because 13^3 is bigger than 2000, secondly, there is no point adding adding numbers below 512 together as you won't get to 1000.

My particular code looped i from 1000, then looped j through the cube numbers, I then kept count of whether i-cube(j) was a cube (bigger than cube(j) - why?). The first number where this happenned twice was 1729. The two ways being 1000+729 and 1+1728.

If there is a purely mathematical way to do it then I would love to know what it is, and would appreciate an email.

Hope that helps,
Kev
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