Search found 303 matches

by tanmoy
Fri Apr 02, 2021 2:34 am
Forum: Algebra
Topic: FE Marathon!
Replies: 96
Views: 4393

Re: FE Marathon!

$\textbf{Problem 24}$ Find all functions $f : \mathbb{N}\rightarrow \mathbb{N}$ satisfying following condition: \[f(n+1)>f(f(n)), \quad \forall n \in \mathbb{N}.\] Source : IMOSL 1977 Actually this is IMO 1977/P6 . Hint: Try to prove that $f(n) \geq n$ $\forall n \in \mathbb{N}$. Then try to prove ...
by tanmoy
Sun Feb 28, 2021 5:26 pm
Forum: News / Announcements
Topic: AoPS and Other Math Books
Replies: 4
Views: 299

Re: AoPS and Other Math Books

Nazifatun Nesa Nahin wrote:
Thu Feb 25, 2021 11:26 pm
From where should I start first?
Which grade are you in?
by tanmoy
Wed Dec 23, 2020 9:49 pm
Forum: Secondary Level
Topic: Problem solution
Replies: 3
Views: 352

Re: Problem solution

Shad wrote:
Wed Dec 23, 2020 12:39 pm
Sorry the total run is 358
Well that doesn't matter much. The answer is still same.
by tanmoy
Wed Dec 23, 2020 9:45 pm
Forum: Algebra
Topic: FE Marathon!
Replies: 96
Views: 4393

Re: FE Marathon!

Putting y= 0 we get, $f(x^4)=x^3f(x) $ How? putting $y = 0$ gives, $\ f(x^4)=x^3f(x) + f(f(0))$ and you didn't prove that $f(f(0)) = 0$. Or, $f(x^4)=f(t)=x^3f(x)\cdots (2)$[Let $x^4=t$] Now from the question we get, $f(x^4+y)=x^3f(x)+f(f(y))$ Or, $f(t+y)=f(t)+f(y)$[Using (1) and (2)] Which is the c...
by tanmoy
Tue Dec 22, 2020 11:46 pm
Forum: Algebra
Topic: FE Marathon!
Replies: 96
Views: 4393

Re: FE Marathon!

I am not sure this solution is correct. Bhaya plz check it if right then I will post a new problem if not then I will probably try more to solve it. Ifx=0 in the given equation, $f(y)=f(f(y))$ Let, $f(t)=q$ for some real t,q Putting y=t in (1) we get, $f(t)=f(f(t))$ Or, $q=f(q)$ Thus, $f(x)=x$ is t...
by tanmoy
Tue Dec 22, 2020 11:32 pm
Forum: Secondary Level
Topic: Problem solution
Replies: 3
Views: 352

Re: Problem solution

The answer is $33$. If all of the $11$ batsmen scored 32 runs, then the total score would be $11 \times 32 = 352$. Since the total score is $358$, at least one batsman needs to score more than $32$ runs. So, the run scored by the highest scorer should be at least $33$. Now, if $5$ batsmen score $32$...
by tanmoy
Mon Dec 21, 2020 1:15 am
Forum: Junior Level
Topic: Please help me solving this problem
Replies: 1
Views: 249

Re: Please help me solving this problem

One of the differences will be $0$. So the product will also become $0$.
by tanmoy
Thu Dec 17, 2020 7:06 pm
Forum: Site Support
Topic: How can I insert images in this forum?
Replies: 1
Views: 265

Re: How can I insert images in this forum?

If you wanna insert image of a geometric figure, you can draw it using https://www.geogebra.org/?lang=en and then attach the file with your post. You can attach any kind of files like below:
Capture.PNG
Capture.PNG (34.61 KiB) Viewed 262 times
by tanmoy
Mon Dec 14, 2020 11:13 pm
Forum: Higher Secondary Level
Topic: একজন আছে যে সবাইকে চিনে।
Replies: 3
Views: 1094

Re: একজন আছে যে সবাইকে চিনে।

Anindya Biswas wrote:
Mon Dec 14, 2020 11:09 pm
Assume there are $3$ peoples. $a$, $b$ and $c$. If $a$ knows $b$, $b$ knows $c$ and $c$ knows $a$. Then the first condition holds but the second condition doesn't!
Assume that knowing is mutual.