Search found 217 matches
- Sat Mar 10, 2012 8:24 pm
- Forum: Algebra
- Topic: interesting fun eq
- Replies: 3
- Views: 2968
interesting fun eq
find all functions f such that for all real x,y \[f:\mathbb{R}\rightarrow \mathbb{R},f(x^3+y^3)=x^2f(x)+yf(y^2)\]
- Sat Mar 10, 2012 7:51 pm
- Forum: Algebra
- Topic: FUN EQUATION
- Replies: 6
- Views: 3634
FUN EQUATION
let \[f:Q\rightarrow Q,\forall x,y \in Q ,f(1)=2,f(xy)=f(x)f(y)-f(x+y)+1\] .find all such functions.
- Sat Mar 10, 2012 4:26 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2004-5
- Replies: 6
- Views: 5431
Re: APMO 2004-5
a,b,c cant assume the value 0.
- Sat Mar 10, 2012 3:05 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2004-5
- Replies: 6
- Views: 5431
Re: APMO 2004-5
is it true that \[(abc)^2+2\geq ab+bc+ca\].
- Sat Mar 10, 2012 10:56 am
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO SL-7(2009)
- Replies: 5
- Views: 3867
Re: IMO SL-7(2009)
oh sorry this only implies f(o)=o
- Sat Mar 10, 2012 2:13 am
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO SL-7(2009)
- Replies: 5
- Views: 3867
Re: IMO SL-7(2009)
plugging x=0 we get f(o)=f(yf(o)).this implies the functional equation is constant.but how?this is an sl prblm
- Sat Mar 10, 2012 12:11 am
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2004
- Replies: 6
- Views: 5482
Re: APMO 2004
we can demonstrate two cases.one of n and n+1 is prime.then the other case is both of them are composite.im not done with the second case.
- Fri Mar 09, 2012 11:53 pm
- Forum: Algebra
- Topic: For begginers Dutch mo1993
- Replies: 2
- Views: 2140
Re: For begginers Dutch mo1993
p=1 or p=-1.just use substitution.
- Thu Mar 08, 2012 2:53 pm
- Forum: Algebra
- Topic: SL 1982 B1
- Replies: 5
- Views: 3185
Re: SL 1982 B1
thank u mahi for latexing.
- Thu Mar 08, 2012 2:52 pm
- Forum: Geometry
- Topic: NICE GEOMETRY PROBLEM
- Replies: 3
- Views: 2538
Re: NICE GEOMETRY PROBLEM
problemta bananor shomoy chintao kori nai polapan coordinate use korbe.