Search found 305 matches

by tanmoy
Wed Apr 21, 2021 7:24 pm
Forum: Introductions
Topic: New to forum
Replies: 2
Views: 183

Re: New to forum

Shown wrote:
Wed Apr 21, 2021 12:59 pm
Hello everyone I am newbie here and I am glad to be part of this community and I also think there is lot of things to learn and gain some knowledge.
Welcome to the forum :)
by tanmoy
Mon Apr 12, 2021 9:27 pm
Forum: Social Lounge
Topic: How to start my math journey?
Replies: 2
Views: 152

Re: How to start my math journey?

Hi I'm Joy. Age of 20. But currently I'm very much interested in math problem solving. So, it would be very helpful if any one give me a list of book for learn the basic of approach for solving a mathematic problem. And also a list of basic topic which I need to learn first. Advance thanks to all o...
by tanmoy
Fri Apr 02, 2021 2:34 am
Forum: Algebra
Topic: FE Marathon!
Replies: 97
Views: 6300

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: 428

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: 435

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: 97
Views: 6300

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: 97
Views: 6300

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: 435

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: 309

Re: Please help me solving this problem

One of the differences will be $0$. So the product will also become $0$.