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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...

$\textbf{Problem 24}$ 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 ...

Nazifatun Nesa Nahin wrote: ↑

Thu Feb 25, 2021 11:26 pm

From where should I start first?

Which grade are you in?

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.

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...

Already posted: viewtopic.php?f=17&t=3262&p=15746#p15746

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...

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 $32$...

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

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