## Rangpur Higher Secondary 2011/5

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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Please don't post problems (by starting a topic) in the "Higher Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
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### Rangpur Higher Secondary 2011/5

Problem 5:
The equation $x^3 +3xy + y^3 = 1$ is solved in nonnegative integers. Find the possible values of $x-y$.

Mehfuj Zahir
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### Re: Rangpur Higher Secondary 2011/5

x-Y=(1,-1).LOOK OVER THE EQN CAREFULLY AND SEE THE CONDITION

Moon
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### Re: Rangpur Higher Secondary 2011/5

Please learn to use LaTeX; it will help you to write equations nicely. (It is actually very easy, most of the times you just need to put your equation between two dollar signs.)

Also please don't write with your caps lock on (I mean in uppercase) unless it is absolutely necessary. Writing in uppercase (almost) means you want to shout at somebody. You can use bold or italic text if you need to stress something. Just avoid writing in uppercase.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

bristy1588
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### Re: Rangpur Higher Secondary 2011/5

Isnt the answer 1 and -1? How come 0 is also the answer?
Bristy Sikder

*Mahi*
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### Re: Rangpur Higher Secondary 2011/5

$x=-1, y=-1$
Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

bristy1588
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Joined: Sun Jun 19, 2011 10:31 am

### Re: Rangpur Higher Secondary 2011/5

Mahi, Question ta dekho okhane bolse non-negative integers, -1 negative integer
Bristy Sikder

nafistiham
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### Re: Rangpur Higher Secondary 2011/5

$(x,y)=(0,1),(1,0)$
so,
$x-y=0,1$
but, how to prove that?
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.