## BdMO National 2012: Higher Secondary 10

Moon
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### BdMO National 2012: Higher Secondary 10

Problem 10:
Consider a function $f: \mathbb{N}_0\to \mathbb{N}_0$ following the relations:
• $f(0)=0$
• $f(np)=f(n)$
• $f(n)=n+f\left ( \left \lfloor \dfrac{n}{p} \right \rfloor \right)$ when $n$ is not divisible by $p$
Here $p > 1$ is a positive integer, $\mathbb{N}_0$ is the set of all nonnegative integers and $\lfloor x \rfloor$ is the largest integer smaller or equal to $x$.
Let, $a_k$ be the maximum value of $f (n)$ for $0\leq n \leq p^k$. Find $a_k$.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

learn how to write equations, and don't forget to read Forum Guide and Rules.

Moon
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Joined: Tue Nov 02, 2010 7:52 pm
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### Re: BdMO National 2012: Higher Secondary 10

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

learn how to write equations, and don't forget to read Forum Guide and Rules.

sourav das
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### Re: BdMO National 2012: Higher Secondary 10

Corei13 used Moon bhaia's method (A direct killing method hi, hi, hi). A different way hint (My contest solution way) (A soft way killing method, ha ha ha)
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

*Mahi*
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### Re: BdMO National 2012: Higher Secondary 10

sourav das wrote:Corei13 used Moon bhaia's method (A direct killing method hi, hi, hi). A different way hint (My contest solution way) (A soft way killing method, ha ha ha)
I did the same as Corei13/moon bhai in both H.Sec 9 and 10
Use $L^AT_EX$, It makes our work a lot easier!