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BdMO Online Forum • Search

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Re: Determine n

Sketch:
Suppose $n$ is such an integer. Prove that $n^2-4=pq^4$ for some prime $p,q$. Deduce that $q=2$.......
by asif e elahi
Fri Jun 02, 2017 8:49 am
 
Forum: Number Theory
Topic: Determine n
Replies: 1
Views: 94

Re: Nice and hard problem!

From the first equation if $y=f(n)^2-458$, then $f(y)=2y^2-2.458^2$
We can rewrite it as $f(y)-2y^2+2.458^2=0$. Suppose $g(y)=f(y)-2y^2+2.458^2$. So $g(y)$ is a polynomial and it has infinite zeros (obviously $f(n)^2-458$ can take infinite values). So $g(y)$ must be zero for all $y$. The rest is easy.
by asif e elahi
Mon May 15, 2017 11:24 am
 
Forum: Algebra
Topic: Nice and hard problem!
Replies: 1
Views: 101

Re: Inequality with abc = 1

Hint:
Prove that
\begin{eqnarray}
\left( x - 1 + \dfrac 1y \right) \left( y - 1 + \dfrac 1z \right)\leq \dfrac{x}{z}
\end{eqnarray}
by asif e elahi
Mon May 15, 2017 11:06 am
 
Forum: Algebra
Topic: Inequality with abc = 1
Replies: 3
Views: 151

Re: Math

Dunno about the first question but if you want to learn directly from Asif E Elahi, I suggest that you start following him on fb. See his timeline and like all of his posts, share them etc etc. Then he might notice you. Also, Asif e Elahi likes eager students. Knock him on messenger/tg and ask for ...
by asif e elahi
Mon Apr 03, 2017 7:55 pm
 
Forum: Social Lounge
Topic: Math
Replies: 7
Views: 436

Re: BDMO Forum Mafia #1

বাচ্চারা অংক করতে যাও
by asif e elahi
Mon Apr 03, 2017 7:53 pm
 
Forum: Social Lounge
Topic: BDMO Forum Mafia #1
Replies: 50
Views: 2003

Re: 2015 regional Secondary no. 6 function algebra

Suppose F(x)=ax+b , then F(F(x))=(a^2)x+ab+b if we compare 4x+3 with (a^2)x+ab+b $F(F(x))$ is not equal to $4x+3$. $F(F(x))=f(f(f(f(x))))$ from your definition of $F$. then we will get F(x)=2x+1 or F(x)=-2x-3 . Considering the next statement we can be sure that F(x)=2x+1 . How do you deduce that? A...
by asif e elahi
Mon Jan 09, 2017 2:23 pm
 
Forum: Algebra
Topic: 2015 regional Secondary no. 6 function algebra
Replies: 4
Views: 210

Re: 2015 regional Secondary no. 6 function algebra

Hint
\begin{align*}
2015=&4\times 503+3\\
503=&4\times 125+3\\
125=&5^3
\end{align*}
by asif e elahi
Sun Jan 08, 2017 2:30 pm
 
Forum: Algebra
Topic: 2015 regional Secondary no. 6 function algebra
Replies: 4
Views: 210

Re: Geometry Marathon : Season 3

Problem 10: Let $I$ be the incenter of $\triangle ABC$. The incircle touches $BC$ at $D$ and $K$ is the antipode of $D$ in $(I)$. Let $M$ be the midpoint of $AI$. Prove that $KM$ passes through the Feuerbach Point . We define some new points 1. $L$ is the midpoint of $BC$ 2. $N$ is the point where ...
by asif e elahi
Sun Jan 08, 2017 4:10 am
 
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 90
Views: 3232

Re: regional mo 2015

Use the Power of Point theorem to prove that $PA\times PD=PE^2=PB\times PC$
by asif e elahi
Tue Dec 13, 2016 12:53 am
 
Forum: Divisional Math Olympiad
Topic: regional mo 2015
Replies: 3
Views: 310

Re: how to solve this??

This is called 'The art gallery problem'.
https://en.wikipedia.org/wiki/Art_gallery_problem
by asif e elahi
Fri Dec 09, 2016 9:05 pm
 
Forum: Junior Level
Topic: Guards in a museum
Replies: 2
Views: 187
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