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)
Dhaka Higher Secondary 2010/1 (Secondary 2010/8)
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.
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.
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
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
Re: Dhaka Higher Secondary 2010/1 (Secondary 2010/8)
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.......
Re: Dhaka Higher Secondary 2010/1 (Secondary 2010/8)
The answer is 0..