Welcome to the forum

## Search found 305 matches

- Wed Apr 21, 2021 7:24 pm
- Forum: Introductions
- Topic: New to forum
- Replies:
**2** - Views:
**162**

- Mon Apr 12, 2021 9:27 pm
- Forum: Social Lounge
- Topic: How to start my math journey?
- Replies:
**2** - Views:
**142**

### 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...

- Fri Apr 02, 2021 2:34 am
- Forum: Algebra
- Topic: FE Marathon!
- Replies:
**97** - Views:
**6192**

### 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 ...

- Sun Feb 28, 2021 5:26 pm
- Forum: News / Announcements
- Topic: AoPS and Other Math Books
- Replies:
**4** - Views:
**416**

### Re: AoPS and Other Math Books

Which grade are you in?

- Wed Dec 23, 2020 9:49 pm
- Forum: Secondary Level
- Topic: Problem solution
- Replies:
**3** - Views:
**420**

- Wed Dec 23, 2020 9:45 pm
- Forum: Algebra
- Topic: FE Marathon!
- Replies:
**97** - Views:
**6192**

### 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...

- Wed Dec 23, 2020 12:13 am
- Forum: Combinatorics
- Topic: A combi salad from mathematical olympiad treasures
- Replies:
**2** - Views:
**454**

- Tue Dec 22, 2020 11:46 pm
- Forum: Algebra
- Topic: FE Marathon!
- Replies:
**97** - Views:
**6192**

### 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...

- Tue Dec 22, 2020 11:32 pm
- Forum: Secondary Level
- Topic: Problem solution
- Replies:
**3** - Views:
**420**

### 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 $32$...

- Mon Dec 21, 2020 1:15 am
- Forum: Junior Level
- Topic: Please help me solving this problem
- Replies:
**1** - Views:
**295**

### Re: Please help me solving this problem

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