## Search found 5 matches

Fri Apr 29, 2016 12:29 pm
Forum: Secondary Level
Topic: Number Theory
Replies: 5
Views: 2628

### Re: Number Theory

According to AM–GM inequality,
$\frac {a+b}{2}$ $\geq\sqrt{ab}$
$\Rightarrow$ $\frac{(a+b)^{2}}{4}$ $\geq ab$
$\Rightarrow (a+b)^{2}\geq 4ab$
$\because (a+b)^{2}\mid 4ab$
$\Rightarrow (a+b)^{2}\leq 4ab$
$\Rightarrow (a+b)^{2}=4ab$
$\therefore (a-b)^{2}=0$
$\therefore a=b$.
Sat Jan 16, 2016 1:17 pm
Forum: Secondary Level
Topic: An Easy Geometry Problem
Replies: 2
Views: 2052

### An Easy Geometry Problem

A triangular pyramid has edge of length $\sqrt{2}$, the
volume is $\frac{a}{b}$ where a, b are co-primes. b-a = ? Sat Jan 09, 2016 11:20 am
Forum: Number Theory
Topic: Number Theory
Replies: 0
Views: 1219

### Number Theory

The number of factor(s) of $(n+1)!$ is double than the number of factor(s) of $n!$. Now, find all non-prime values of $(n+1)$.
Fri Sep 04, 2015 9:13 pm
Forum: International Mathematical Olympiad (IMO)
Topic: IMO 2000/1
Replies: 6
Views: 3137

### Re: IMO 2000/1

As $AB || CD$, we get $\angle EBA = \angle EDC$. Again by Alternate Segment Theorem, $\angle ABM = \angle BDM$. So, $\angle EBA = \angle ABM$. Similarly we get $\angle EAB = \angle BAM$. So,we get $\triangle EBA \cong \triangle ABN$ by the ASA theorem. Then, we get $EN \perp AB.$ Now, let the segme...
Thu Aug 27, 2015 11:05 pm
Forum: National Math Camp
Topic: Exam 2, Online Number Theory Camp, 2015
Replies: 24
Views: 13137

### Re: Exam 2, Online Number Theory Camp, 2015

৯ টা বাজে না ক্যারে?