Search found 217 matches

by zadid xcalibured
Wed Jan 09, 2013 7:49 pm
Forum: Geometry
Topic: IMO 2007 Problem 4
Replies: 4
Views: 8931

Re: IMO 2007 Problem 4

The result follows by proving $RP=QC$ and showing $\triangle{LCQ}$ and $\triangle{PKC}$ similar
by zadid xcalibured
Sun Jan 06, 2013 6:15 pm
Forum: Introductions
Topic: Hello Everybody
Replies: 3
Views: 2365

Re: Hello Everybody

Hello everyone.I am Zadid Hasan from the town of Mymensingh,Bangladesh.I joined this forum on Oct 27,2011.My present favourite color is BLUE. :mrgreen:
Btw welcome charityst021. :D :D :D
Tiham,What do you mean your forum? :evil:
Having post number too high doesn't make it yours. :twisted:
by zadid xcalibured
Fri Jan 04, 2013 10:14 pm
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 58748

Re: Secondary and Higher Secondary Marathon

Some moderator edit this.
by zadid xcalibured
Thu Jan 03, 2013 2:44 pm
Forum: Number Theory
Topic: IMO Shortlist 2007 N1
Replies: 2
Views: 1273

Re: IMO Shortlist 2007 N1

My steps:
Adib's steps. :mrgreen:
by zadid xcalibured
Thu Jan 03, 2013 2:41 pm
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 58748

Re: Secondary and Higher Secondary Marathon

Here goes another easy one.
Problem $23$:Find all continuous functions from the set of real numbers to itself satisfying $f(x + y) = f(x) + f(y) + f(x)f(y)$.
by zadid xcalibured
Thu Jan 03, 2013 3:08 am
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 58748

Re: Secondary and Higher Secondary Marathon

It seems you folks lack stamina for a marathon.But resting is enough already i suppose.Let the marathon commence again with an easier problem. Problem $22$:Let $CH$ be the altitude of triangle $ABC$ with $∠ACB = 90°$. The bisector of $∠BAC$ intersects $CH$, $CB$ at $P$, $M$ respectively. The bisecto...
by zadid xcalibured
Fri Dec 21, 2012 3:52 am
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 58748

Re: Secondary and Higher Secondary Marathon

Problem $21$: Determine all positive rationals $x,y,z$ such that $x+y+z$,$xyz$,$\frac{1} {x}+\frac{1} {y}+\frac{1} {z}$ are all integers.
by zadid xcalibured
Fri Dec 21, 2012 12:47 am
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 127
Views: 58748

Re: Secondary and Higher Secondary Marathon

This sequence must be periodic with period at most $9$.Actually this is periodic with period $6$.So $A(30)=A(6)=77777770000000$
by zadid xcalibured
Wed Dec 19, 2012 3:40 pm
Forum: International Mathematical Olympiad (IMO)
Topic: IMO Marathon
Replies: 184
Views: 64124

Re: IMO Marathon

To revive the marathon here goes a problem.
Problem $14$:Let $a$ and $b$ be positive integers such that $a^n +n$ divides $b^n +n$ for
every positive integer $n$. Show that $a = b$.