Suppose $n$ is such an integer. Prove that $n^2-4=pq^4$ for some prime $p,q$. Deduce that $q=2$.......

Sketch:

- Fri Jun 02, 2017 8:49 am
- Forum: Number Theory
- Topic: Determine n
- Replies:
**1** - Views:
**159**

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.

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.

- Mon May 15, 2017 11:24 am
- Forum: Algebra
- Topic: Nice and hard problem!
- Replies:
**1** - Views:
**153**

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 ...

- Mon Apr 03, 2017 7:55 pm
- Forum: Social Lounge
- Topic: Math
- Replies:
**7** - Views:
**592**

বাচ্চারা অংক করতে যাও

- Mon Apr 03, 2017 7:53 pm
- Forum: Social Lounge
- Topic: BDMO Forum Mafia #1
- Replies:
**51** - Views:
**2620**

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...

- Mon Jan 09, 2017 2:23 pm
- Forum: Algebra
- Topic: 2015 regional Secondary no. 6 function algebra
- Replies:
**4** - Views:
**301**

- Sun Jan 08, 2017 2:30 pm
- Forum: Algebra
- Topic: 2015 regional Secondary no. 6 function algebra
- Replies:
**4** - Views:
**301**

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 ...

- Sun Jan 08, 2017 4:10 am
- Forum: Geometry
- Topic: Geometry Marathon : Season 3
- Replies:
**109** - Views:
**4821**

Use the Power of Point theorem to prove that $PA\times PD=PE^2=PB\times PC$

- Tue Dec 13, 2016 12:53 am
- Forum: Divisional Math Olympiad
- Topic: regional mo 2015
- Replies:
**3** - Views:
**397**

This is called 'The art gallery problem'.

https://en.wikipedia.org/wiki/Art_gallery_problem

https://en.wikipedia.org/wiki/Art_gallery_problem

- Fri Dec 09, 2016 9:05 pm
- Forum: Junior Level
- Topic: Guards in a museum
- Replies:
**2** - Views:
**229**