## Search found 66 matches

- Sun Apr 08, 2012 9:43 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: ISL 2003
- Replies:
**12** - Views:
**3948**

### Re: ISL 2003

Can u please send me a msg about the question of APMO 4?I have forgot the question

- Sun Apr 08, 2012 8:03 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: ISL 2003
- Replies:
**12** - Views:
**3948**

### ISL 2003

Three distinct points $A,B,C$ are fixed on a line in this order.Denote by P the intersection of the tangents to a circle at $A$ and $C$ where the centre of the circle doesn't lie on the line $AC$.Suppose, $Q$ is intersection point of the segment $PB$ and the circle.Prove that the intersection of the...

- Sat Apr 07, 2012 8:03 pm
- Forum: Number Theory
- Topic: সংখ্যার অঙ্ক
- Replies:
**1** - Views:
**854**

### Re: সংখ্যার অঙ্ক

Let the product of the digits of $n$ be $P(n)$. It is easy to prove that $P(n)\leq n$. So write $P(n)=n - k$ where $k \in \mathbb {N}$. So we get the quadratic equation $n^2 - 10n - 22=n - k$ the determinant of which must be a perfect square.Plugging the convenient values of $k$ and examining the r...

- Sat Apr 07, 2012 2:15 pm
- Forum: Number Theory
- Topic: সংখ্যার অঙ্ক
- Replies:
**1** - Views:
**854**

### সংখ্যার অঙ্ক

Find all positive integers $n$ the product of whose digits is equal to $n^2 - 10n - 22$

- Fri Apr 06, 2012 8:04 pm
- Forum: National Math Camp
- Topic: BOMC-2012 Test Day 1
- Replies:
**24** - Views:
**7907**

### Re: BOMC-2012 Test Day 1

নায়েল ভাইয়াকে প্রাইভেট মেসেজ পাঠাবো কীভাবে?

- Sun Apr 01, 2012 5:55 am
- Forum: National Math Camp
- Topic: Not so easy (Camp problems) (BOMC-2)
- Replies:
**6** - Views:
**2658**

### Re: Not so easy (Camp problems) (BOMC-2)

Can u help me?i only have mobile to go to internet.i can't download pdf files

- Sun Apr 01, 2012 12:08 am
- Forum: National Math Camp
- Topic: Advanced P-1 (BOMC-2)
- Replies:
**10** - Views:
**3698**

- Sat Mar 31, 2012 10:04 pm
- Forum: National Math Camp
- Topic: Advanced P-1 (BOMC-2)
- Replies:
**10** - Views:
**3698**

- Sat Mar 31, 2012 10:00 pm
- Forum: National Math Camp
- Topic: Advanced P-1 (BOMC-2)
- Replies:
**10** - Views:
**3698**

- Sat Mar 31, 2012 9:57 pm
- Forum: National Math Camp
- Topic: Advanced P-1 (BOMC-2)
- Replies:
**10** - Views:
**3698**

### Re: Advanced P-1 (BOMC-2)

Intuition Seeing the problem,first thing came into my mind is quadratic residue.So far I have been able to solve the first two cases.For the first case,take (mod 3).U will only have 2 know that 2 is not a quadratic residue (mod 3).For the second case,take mod 4.u will only have to know that 2 isn't ...