Advanced P-1 (BOMC-2)
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1. (a) Prove that the sum of the squares of $3, 4, 5,$ or $6$ consecutive integers
is not a perfect square.
(b) Give an example of $11$ consecutive positive integers the sum of whose
squares is a perfect square.
is not a perfect square.
(b) Give an example of $11$ consecutive positive integers the sum of whose
squares is a perfect square.
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......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
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Re: Advanced P-1 (BOMC-2)
Intuition says:
for (a)
for (b)
I think my intuitions contain a high level of hint. So first please, try to make your own intuitions first, then if you really get stuck, share your intuitions with us and get some intuitions from us...
for (a)
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......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
- Niloy Da Fermat
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- Niloy Da Fermat
- Posts:33
- Joined:Wed Mar 21, 2012 11:48 am
Re: Advanced P-1 (BOMC-2)
b.
so far i have made
note: i made calculation error in this modular equation
so far i have made
Last edited by Niloy Da Fermat on Sun Apr 01, 2012 2:25 am, edited 1 time in total.
kame......hame.......haa!!!!
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Re: Advanced P-1 (BOMC-2)
@ Niloy
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......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
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Re: Advanced P-1 (BOMC-2)
Intuition
Moderator's comment: Try to post all your works in Hidden text
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Re: Advanced P-1 (BOMC-2)
Last edited by *Mahi* on Sat Mar 31, 2012 10:03 pm, edited 1 time in total.
Reason: Don't post your thought in open sight, hide them man!
Reason: Don't post your thought in open sight, hide them man!
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Re: Advanced P-1 (BOMC-2)
Last edited by *Mahi* on Sat Mar 31, 2012 10:08 pm, edited 1 time in total.
Reason: Add [hide] and [/hide] before and after your solution to hide them. It is very possible to do so from mobile.
Reason: Add [hide] and [/hide] before and after your solution to hide them. It is very possible to do so from mobile.
- nafistiham
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Re: Advanced P-1 (BOMC-2)
for b
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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.