Search found 5 matches

by Soumitra Das
Tue Apr 03, 2018 11:57 pm
Forum: Number Theory
Topic: A Conjecture
Replies: 1
Views: 312

A Conjecture

Prove that for every prime $$p > 2$$,there exists a prime $$q < p$$ such that $$p-q = 2^n$$ for some $n \in N_0$.
by Soumitra Das
Mon Sep 25, 2017 3:48 am
Forum: National Math Camp
Topic: National Camp 2016
Replies: 1
Views: 871

Re: National Camp 2016

If $ABC$ is an arbitrary triangle and the value of $n$ satisfies the given condition,obviously it will be also true for certain $ABC$.Consider a triangle $ABC$ with angle $$A=120$$, $$AB=AC$$, circumcenter $O$, midpoint of $$AB=M$$, midpoint of $$AC=N$$, center of the regular polygon constructed out...
by Soumitra Das
Wed Apr 05, 2017 7:51 pm
Forum: Number Theory
Topic: Perfect Cube
Replies: 1
Views: 618

Re: Perfect Cube

Here I want to use a simple lemma,which is: Let a,b,c,d be some integer s.t. (a,b)=(c,d)=1.When $$\frac{a}{b}+\frac{c}{d}=n$$,where n \in N,then |b|=|d| It's proof is simple,first prove b|d and second d|b Proof of the original problem: First,assume (a,b,c)=1.Let (a,b)=x,(b,c)=y,(c,a)=z. $$\frac{a}{b...
by Soumitra Das
Wed Apr 05, 2017 2:29 pm
Forum: National Math Olympiad (BdMO)
Topic: BDMO 2017 National round Secondary 6
Replies: 9
Views: 1316

Re: BDMO 2017 National round Secondary 6

We can rotate the octahedron by 8\times3 or 24 ways(to prove it,just assign one side of the octahedron as A and one of it's neighbour as B and observe it's rotation). So,the total number of distinguishable octahedron is \frac{8!}{24} or 1680.
by Soumitra Das
Wed Apr 05, 2017 1:37 pm
Forum: Combinatorics
Topic: Binary Representation
Replies: 0
Views: 441

Binary Representation

Let for any positive integer $n$,$B(n)$ be the number of 1's in it's binary representation.Prove that $$B(nm) \geq \max{B(n),B(m)}$$ ,where $n,m \in N$ .