divisibility of integers

[rattan123]

show that any integer divisible by 3 can be written as a sum of of cubes of 4 integers.(example 6=2^3+ (-1)^3 + (-1)^3 +0^3 )

[adthedaddy]

Some examples -

9= 2^3+(1)^3+(-1)^3+(1)^3
12=3^3+(-2)^3+(-2)^3+(1)^3

By the way what is your question ? Do you need examples to validate the question ?

[rattan123]

i need a proof..

[Brent@GMATPrepNow]

show that any integer divisible by 3 can be written as a sum of of cubes of 4 integers.(example 6=2^3+ (-1)^3 + (-1)^3 +0^3 )

Hey rattan123,

What's the source of these questions? Given that they're obviously not GMAT questions, I'm getting the strange impression that you're asking us to help you with your math homework.

Cheers,
Brent

[rattan123]

The source is excursion in mathematics..exercise 1.1 question 15

[Brent@GMATPrepNow]

The source is excursion in mathematics..exercise 1.1 question 15

I think it's a good idea to refrain from posting question that are outside the scope of the GMAT. The main reason for this is that many students in the early (or even late) stages of their GMAT preparation do not know how to identify legitimate GMAT questions. So, when they come across some of the questions that you've posted they become concerned and may also lose some confidence in their abilities. Even worse, they may go out and try to learn concepts that are not tested on the GMAT. This would be a tremendous waste of time for people who are already spending a significant amount of time preparing for this challenging test.

Cheers,
Brent