Advanced P-3(BOMC-2)
-
- Posts:461
- Joined:Wed Dec 15, 2010 10:05 am
- Location:Dhaka
- Contact:
Most positive integers can be expressed as a sum of two or more consecutive
positive integers. For example, $24 = 7 + 8 + 9$ and $51 = 25 + 26$. A
positive integer that cannot be expressed as a sum of two or more consecutive
positive integers is therefore interesting. What are all the interesting
integers?
positive integers. For example, $24 = 7 + 8 + 9$ and $51 = 25 + 26$. A
positive integer that cannot be expressed as a sum of two or more consecutive
positive integers is therefore interesting. What are all the interesting
integers?
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......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Advanced P-3(BOMC-2)
Sharing Hints:
First and most basic idea:
Then:
Then:
And then... problem solved.
(Open the hints in three stages, not all in once. This is because it is easier to get the later hints when you know the earlier ones.)
First and most basic idea:
(Open the hints in three stages, not all in once. This is because it is easier to get the later hints when you know the earlier ones.)
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
- Niloy Da Fermat
- Posts:33
- Joined:Wed Mar 21, 2012 11:48 am
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: Advanced P-3(BOMC-2)
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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.
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: Advanced P-3(BOMC-2)
I did not have the proof yesterday.today, I think I do.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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.
-
- Posts:461
- Joined:Wed Dec 15, 2010 10:05 am
- Location:Dhaka
- Contact:
Re: Advanced P-3(BOMC-2)
Really nice trick . But i think there is a bug. Try to find it out.nafistiham wrote:I did not have the proof yesterday.today, I think I do.
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......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
- zadid xcalibured
- Posts:217
- Joined:Thu Oct 27, 2011 11:04 am
- Location:mymensingh
Re: Advanced P-3(BOMC-2)
nice thinking tiham.but it holds for very large numbers only.
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: Advanced P-3(BOMC-2)
thanks to zadid, found out that the numbers which has a large divisor in the form $2^k$ will have problem.because in those cases.$(m-s)$ might be negative.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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: Advanced P-3(BOMC-2)
@Tiham:
Add theseTo you solution , and see what you get. It improves the precision.
Add these
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