Dhaka Higher Secondary 2010/1 (Secondary 2010/8)

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Higher Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

Dhaka Higher Secondary 2010/1 (Secondary 2010/8)

Assume, $\Phi : A \to A, A=\{0,1,2,\cdots \}$ is a function, which is defined as,
$\Phi(x) = \begin{cases} 0 \quad \text{if } x \text{ is a prime}\\ \Phi(x - 1) \quad \text{if } x \text{ is not a prime} \end{cases}$
Find $\sum_{x=2}^{2010} \Phi(x)$

(Corrected)

tushar7
Posts: 101
Joined: Tue Dec 07, 2010 3:23 pm

Re: Dhaka Higher Secondary 2010/1

is this BDMO bot user like gamebot in AOPS ,
the problem was corrected from $x=2$ to 2010 not $x=0$
the aswer is 0 for every $x$ will be $f(x)=0$ ,even if we think $2$ is only prime number

Shifat
Posts: 53
Joined: Sun Jul 31, 2011 12:21 pm
I have no idea about summations, Do not even know what does the symbols and variables mean there( I beg someone teach me what are they, physics give me a lot of trouble for this), but comin to the function, for any number n, if it is prime then $\phi (n)$ is 0, and if it is not prime then it will continue to go $\phi (n-1)$ .. until it gets prime, and then it gets 0 as well!!! (I hope I got the question and concept right) so ultimately for any n, $\phi (n)$ =0!!! now please clear e the summation thing so that I can atleast try to post a solution.......