Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2008-07-05 06:25:40
- tony123
- Member
- Registered: 2007-08-03
- Posts: 229
Square
prove that
is a Square
with
a positive integerLast edited by tony123 (2008-07-05 06:59:24)
Offline
#2 2008-07-05 06:49:20
- Daniel123
- Member
- Registered: 2007-05-23
- Posts: 663
Re: Square
It's not...
....???
Last edited by Daniel123 (2008-07-05 06:50:39)
Offline
#3 2008-07-05 07:00:02
- tony123
- Member
- Registered: 2007-08-03
- Posts: 229
Re: Square
im sory
a positive integerOffline
#4 2008-07-05 20:51:19
- Kurre
- Member
- Registered: 2006-07-18
- Posts: 280
Re: Square
iirc this problem is considered one of the most difficult problems ever submitted in the IMO...:O
Offline
#5 2008-07-06 00:24:42
- ZHero
- Real Member
- Registered: 2008-06-08
- Posts: 1,889
Re: Square
The equation has only solution N=m=n=1 !
Consider..
(m^2+n^2)/(mn+1)
upon actual division, we get remainder equal to (n/m-m/n) which should be 0 (because its less than mn+1)for N to be an integer!
So, (n/m-m/n)=0
or, m=n
hence, N=2m^2/(m^2+1)
which on division gives the remainder as 2=/=0
therefore, for N to be integer, divisor must divide 2 which is possible only when m^2+1=2 or m=1 (all numbers are positive)!
Which gives N=1 which is of course a square!
any comments are welcome!
BTW, would anyone please be kind enough to take a little pain in teaching me how to write the codes for the above equations to make them look more tidy??
Last edited by ZHero (2008-07-06 00:28:49)
If two or more thoughts intersect, there has to be a point!
Offline
#6 2008-07-06 00:33:56
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: Square
The equation has only solution N=m=n=1 !
Youre wrong.
Offline
#7 2008-07-06 00:45:54
- ZHero
- Real Member
- Registered: 2008-06-08
- Posts: 1,889
Re: Square
Wow!
I always thought that maths was never easy!!
anyways, lemme check if i've got how to write the above..
Last edited by ZHero (2008-07-06 01:39:47)
If two or more thoughts intersect, there has to be a point!
Offline
#8 2008-07-06 00:47:12
- ZHero
- Real Member
- Registered: 2008-06-08
- Posts: 1,889
Re: Square
Heck!
Where am i going wrong??:o
If two or more thoughts intersect, there has to be a point!
Offline
#9 2008-07-06 01:35:55
- tony123
- Member
- Registered: 2007-08-03
- Posts: 229
Re: Square
use[ ][/ ] , don t use [/ ] [/ ]
Last edited by tony123 (2008-07-06 01:38:29)
Offline
#10 2008-07-06 01:44:32
- ZHero
- Real Member
- Registered: 2008-06-08
- Posts: 1,889
Re: Square
use[ ][/ ] , don t use [/ ] [/ ]
oooh!
I edited the earlier post and ITS WORKING!
Thanks tony123!
And, i've seen that MOST of your questions are unanswered and they obviously are from Olympiads... Right?
Well, where from do you get these questions?
And if you know the solution to any of those, then do enlighten us too!
The questions are really really amazing and i must say "they add to the beauty of mathematics!!"
If two or more thoughts intersect, there has to be a point!
Offline
#11 2008-07-06 01:48:08
- ZHero
- Real Member
- Registered: 2008-06-08
- Posts: 1,889
Re: Square
Anyways, here's something!
and for N to be square, at least one of N, m, n should be 2!
And it can't be N!
What next?
If two or more thoughts intersect, there has to be a point!
Offline
Pages: 1