Search found 66 matches

by shehab ahmed
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
by shehab ahmed
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...
by shehab ahmed
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...
by shehab ahmed
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 $n^2 - 10n - 22$
by shehab ahmed
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?
by shehab ahmed
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
by shehab ahmed
Sun Apr 01, 2012 12:08 am
Forum: National Math Camp
Topic: Advanced P-1 (BOMC-2)
Replies: 10
Views: 3698

Re: Advanced P-1 (BOMC-2)

I found two such sequence of 11 consecutive integers.One of them has 23 as its median and the other has 43 as its median.
by shehab ahmed
Sat Mar 31, 2012 10:04 pm
Forum: National Math Camp
Topic: Advanced P-1 (BOMC-2)
Replies: 10
Views: 3698

Re: Advanced P-1 (BOMC-2)

Also among 6 positive integers,three of them must be odd and the result follows
by shehab ahmed
Sat Mar 31, 2012 10:00 pm
Forum: National Math Camp
Topic: Advanced P-1 (BOMC-2)
Replies: 10
Views: 3698

Re: Advanced P-1 (BOMC-2)

For the third,taking (mod 4) kills it.because,among 5 consecutive integers,either 3 of them is odd or 2 of them is odd
by shehab ahmed
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 ...