Rangpur Higher Secondary 2011/5
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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 $xy$.
The equation $x^3 +3xy + y^3 = 1$ is solved in nonnegative integers. Find the possible values of $xy$.

 Posts: 78
 Joined: Thu Jan 20, 2011 10:46 am
Re: Rangpur Higher Secondary 2011/5
xY=(1,1).LOOK OVER THE EQN CAREFULLY AND SEE THE CONDITION
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.
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.
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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 Joined: Sun Jun 19, 2011 10:31 am
Re: Rangpur Higher Secondary 2011/5
Isnt the answer 1 and 1? How come 0 is also the answer?
Bristy Sikder
Re: Rangpur Higher Secondary 2011/5
$x=1, y=1$
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah  Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah  Mahi
 bristy1588
 Posts: 92
 Joined: Sun Jun 19, 2011 10:31 am
Re: Rangpur Higher Secondary 2011/5
Mahi, Question ta dekho okhane bolse nonnegative integers, 1 negative integer
Bristy Sikder
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Re: Rangpur Higher Secondary 2011/5
\[(x,y)=(0,1),(1,0)\]
so,
\[xy=0,1\]
but, how to prove that?
so,
\[xy=0,1\]
but, how to prove that?
\[\sum_{k=0}^{n1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please cooperate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please cooperate.