divisibility of integers

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rattan123: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sun Nov 13, 2011 6:19 am

by rattan123 » Wed Aug 15, 2012 8:42 am

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 )

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Source: Beat The GMAT — Problem Solving | Wed Aug 15, 2012 8:42 am

adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pmFollowed by: 3 members; Thanked: 39 times

by adthedaddy » Wed Aug 15, 2012 8:52 am

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 ?

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rattan123: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sun Nov 13, 2011 6:19 am

by rattan123 » Wed Aug 15, 2012 6:29 pm

i need a proof..

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 15, 2012 7:08 pm

rattan123 wrote: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

Brent Hanneson - Creator of GMATPrepNow.com

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rattan123: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sun Nov 13, 2011 6:19 am

by rattan123 » Wed Aug 15, 2012 10:12 pm

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Aug 16, 2012 6:19 am

rattan123 wrote: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

Brent Hanneson - Creator of GMATPrepNow.com

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