Imo 2010-1
Find all functions $f:\mathbb R \to \mathbb R$ such that for all $x,y\in \mathbb R$ $f([x]y)=f(x)f([y])$ where $[a]$ denots the greatest integer less than or equal $a$
One one thing is neutral in the universe, that is $0$.
Re: Imo 2010-1
Ahh...a nice problem that gave me 5 imo points Here is my solution:
Every logical solution to a problem has its own beauty.
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Re: Imo 2010-1
I have a question in Case 2.2 .
If $0<y<1$ then, how can i express the integers (not $0$) in form of \[\left \lfloor x \right \rfloor y\]
[I had this question when i saw the solution in newspaper ]
If $0<y<1$ then, how can i express the integers (not $0$) in form of \[\left \lfloor x \right \rfloor y\]
[I had this question when i saw the solution in newspaper ]
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: Imo 2010-1
Let $\frac x {\left \lfloor x \right \rfloor} = y$sourav das wrote:I have a question in Case 2.2 .
If $0<y<1$ then, how can i express the integers (not $0$) in form of \[\left \lfloor x \right \rfloor y\]
[I had this question when i saw the solution in newspaper ]
Now,for all real $x$ , $0< y \leq 1$ (I think you can see why)
(Again a thing you should notice, $x,y$ are real numbers , not necessarily integers. )
@Zzzz Vai
2 mark kata gesilo keno?
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Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi