Search found 264 matches
- Fri Dec 04, 2020 7:09 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2020 P7
- Replies: 2
- Views: 3412
Re: BdMO National Secondary 2020 P7
Claim-1: $f(1)=1$ Proof : it follows directly from the definition when $n=1$. Claim-2: $f(p)=p$ for all prime $p$ Proof: Let's substitute $n=p$ where $p$ is a prime number in the given equation, we get: $$p=f(p)f(1)$$. $$\therefore p=f(p)$$ since $f(1)=1$. (Proved) Claim-3: $f(p^k)=p$ for all prime...
- Thu Dec 03, 2020 10:07 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2020 P6
- Replies: 2
- Views: 3667
Re: BdMO National Secondary 2020 P6
An almost sorted permutation would look like this: (a sorted permutaion)-(suddenly a number which is less than the previous)-(again a sorted permutation) . For example : $(1,3,5,2,4,6)$. Here $(1,3,5)$ was increasing, then the number $2$ is a sudden drop in that increasing pattern. Then again $(2,4,...
- Thu Dec 03, 2020 9:38 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2020 P3
- Replies: 1
- Views: 3899
Re: BdMO National Secondary 2020 P3
Let's consider the peoples as vertices and handshakes as edges of a graph. We will connect $A$ and $B$ with an edge if $A$ handshakes with $B$. So this graph has $11$ nodes. Now, we will take the complete graph with $11$ vertices and start removing edges in such a way that each triplet of vertices c...
- Fri Oct 02, 2020 11:34 pm
- Forum: Computer Science
- Topic: Programming LOGARITHM
- Replies: 1
- Views: 8433
Re: Programming LOGARITHM
Try this: If $y=10^{n+\frac{a_1}{10}+\frac{a_2}{10^2}+\cdots}$ where $a_1,a_2,\cdots$ are digits, then $n.a_1a_2\cdots=\log_{10}{y}$. Now $n$ is simply the number of times you have to divide $y$ to get a number greater than or equal to $1$ and less than $10$. Here is a recursive relationship to get ...