Let $d$ be any positive integer not equal to $2, 5, $ or $13$. Show that one can find
distinct $a, b$ in the set {$2, 5, 13, d$} such that $ab − 1$ is not a perfect square.
Advanced P-6(BOMC-2)
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You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
- nafistiham
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Re: Advanced P-6(BOMC-2)
I am really confused. How can it be where $2\cdot5-1=3^2,2\cdot13-1=5^2,13\cdot5-1=8^2$
I think I am lost somewhere.please clarify.
I think I am lost somewhere.please clarify.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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.
- Niloy Da Fermat
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Re: Advanced P-6(BOMC-2)
এই সেট থেকে ৬ টা $ ab-1 $ পাওয়া যাবে ।প্রমাণ করতে হবে এর ভিতর অন্তত ১টা (সবগুলো হওয়ার দরকার নেই) perfect square হবে না ।nafistiham wrote:I am really confused. How can it be where $2\cdot5-1=3^2,2\cdot13-1=5^2,13\cdot5-1=8^2$
I think I am lost somewhere.please clarify.
Last edited by Niloy Da Fermat on Sun Apr 01, 2012 3:01 am, edited 1 time in total.
kame......hame.......haa!!!!
- Niloy Da Fermat
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Re: Advanced P-6(BOMC-2)
sorry for using bangla.but without it, i possibly couldn't clarify.
an example:if $ 13d-1 $ is not perfect square, that is enough
an example:if $ 13d-1 $ is not perfect square, that is enough
kame......hame.......haa!!!!
Re: Advanced P-6(BOMC-2)
General Hint:
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