বজ্জাত z কে মারার জন্য ১০০০ থ্যাঙ্কস ঘোষণা করা হল (BOMC-2)
- Niloy Da Fermat
- Posts:33
- Joined:Wed Mar 21, 2012 11:48 am
find all integral solutions $ (x,y,z) $ of $ x^2-y^2=2xyz $
kame......hame.......haa!!!!
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: বজ্জাত z কে মারার জন্য ১০০০ থ্যাঙ্কস ঘোষণা করা হল (BOMC-
Pardon me.But, I find the topic name a little odd.Any reason behind this type of name ?Niloy Da Fermat wrote:find all integral solutions $ (x,y,z) $ of $ x^2-y^2=2xyz $
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: বজ্জাত z কে মারার জন্য ১০০০ থ্যাঙ্কস ঘোষণা করা হল (BOMC-
Let $(x,y)=g$ and $x=gx',y=gy'$Niloy Da Fermat wrote:find all integral solutions $ (x,y,z) $ of $ x^2-y^2=2xyz $
So $ x'^2-y'^2=2x'y'z $ which implies $x'|y'^2$ and $y'|x'^2$ or $x'=y'=1$,
Which implies $xyz=0$ which means $z=0$ or $x=y=0$.
Please read Forum Guide and Rules before you post.
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
Re: বজ্জাত z কে মারার জন্য ১০০০ থ্যাঙ্কস ঘোষণা করা হল (BOMC-
Here's a another approach:
we can rewrite the equation, 2z=(x/y-y/x)
let x/y=n
so, 2z=n-1/n
it implies that, n=1.
That means, x=y and z=0
Therefore, (x,y,z)=(k,k,0) for any integer k.
we can rewrite the equation, 2z=(x/y-y/x)
let x/y=n
so, 2z=n-1/n
it implies that, n=1.
That means, x=y and z=0
Therefore, (x,y,z)=(k,k,0) for any integer k.
Re: বজ্জাত z কে মারার জন্য ১০০০ থ্যাঙ্কস ঘোষণা করা হল (BOMC-
*Mahi* wrote:Let $(x,y)=g$ and $x=gx',y=gy'$Niloy Da Fermat wrote:find all integral solutions $ (x,y,z) $ of $ x^2-y^2=2xyz $
So $ x'^2-y'^2=2x'y'z $ which implies $x'|y'^2$ and $y'|x'^2$ or $x'=y'=1$,
Which implies $xyz=0$ which means $z=0$ or $x=y=0$.
bujhlam na.....
Your defense shatters;
The life bar drains to red, then...
Nothing. Game over.
The life bar drains to red, then...
Nothing. Game over.
Re: বজ্জাত z কে মারার জন্য ১০০০ থ্যাঙ্কস ঘোষণা করা হল (BOMC-
কোনও উত্তর নাই!!!
Your defense shatters;
The life bar drains to red, then...
Nothing. Game over.
The life bar drains to red, then...
Nothing. Game over.
Re: বজ্জাত z কে মারার জন্য ১০০০ থ্যাঙ্কস ঘোষণা করা হল (BOMC-
Please elaborate, exactly which part is your problem. We can't explain a solution if we don't know which part seems obscure.Xenon96 wrote: কোনও উত্তর নাই!!!
Please read Forum Guide and Rules before you post.
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