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Re: Prime numbers

$n$=$2,5,7$.
by aritra barua
Sat Dec 16, 2017 7:37 pm
 
Forum: Number Theory
Topic: Prime numbers
Replies: 2
Views: 52

Re: Yet divisibility...

This is an IMO $1994$ problem.Look up the problem in $AoPS$.
by aritra barua
Wed Dec 13, 2017 8:45 pm
 
Forum: Number Theory
Topic: Yet divisibility...
Replies: 6
Views: 409

Re: A strange NUMBER THEORY Problem

The $3rd$ number begets an answer of $-1$ which isn't a natural number.
by aritra barua
Mon Dec 11, 2017 1:55 pm
 
Forum: Higher Secondary Level
Topic: A strange NUMBER THEORY Problem
Replies: 3
Views: 68

Re: Beginner's Marathon

Problem $26$
Given an acute angled triangle $\bigtriangleup ABC$.Inscribe in it a triangle $UVW$ of least possible perimeter.
by aritra barua
Fri Jul 07, 2017 1:08 pm
 
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 3756

Re: More primes and more primes!

Apparently,this is a TST problem from Hong Kong.We rewrite our equation:$2^m*p^2$=$y^7-1$=$(y-1)(y^6+y^5....+y+1)$.Clearly $y$ being odd implies $y^6+y^5...+y+1$ is odd.Hence $2^m$ must divide $y-1$ since $p$ is a positive integer.Now the equation $\frac{y-1}{2^m}$*$(y^6+y^5...+y+1)$=$p^2$ leads us ...
by aritra barua
Fri Jul 07, 2017 10:45 am
 
Forum: Number Theory
Topic: More primes and more primes!
Replies: 1
Views: 243

More primes and more primes!

Find every triplet of positive integers ($m,p,y$) such that the equation:$2^m*p^2+1$=$y^7$ is satisfied when $p$ and $y$ are primes.
by aritra barua
Wed Jul 05, 2017 7:55 pm
 
Forum: Number Theory
Topic: More primes and more primes!
Replies: 1
Views: 243

Infinite solutions

Find with proof every pair of ($a$,$b$) in general form such that $a+b^2$|$a^3+b^3$.
by aritra barua
Tue Jul 04, 2017 7:46 pm
 
Forum: Number Theory
Topic: Infinite solutions
Replies: 1
Views: 219

IMO 2009 SL(G-1)

Let $\bigtriangleup$ $ABC$ be an isosceles triangle with $AB$=$AC$.The bisectors of $\angle BAC$ and $\angle ABC$ intersect $BC$ and $AC$ at $D$ and $E$ respectively.Suppose $\angle BEK$ to be $45$ degree,where $K$ is the incenter of $\bigtriangleup$ $ACD$.Determine all possible values of $\angle BA...
by aritra barua
Mon Jun 19, 2017 3:02 pm
 
Forum: Geometry
Topic: IMO 2009 SL(G-1)
Replies: 1
Views: 227

Re: Beginner's Marathon

What has been meant by 'after 2 hours 30 min'?
by aritra barua
Thu Jun 15, 2017 2:44 pm
 
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 3756

Re: Beginner's Marathon

An easy problem:$\text{Problem 20}$
The fractions $\frac{7x+1}{2}$, $\frac{7x+2}{3}$,......., $\frac{7x+2016}{2017}$ are irreducible.Find all possible values of $x$ such that $x$ is less than or equal to $300$.This Problem was recommended by Zawad bhai in a mock test at CMC.
by aritra barua
Fri Jun 09, 2017 4:27 pm
 
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 3756
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