Search found 57 matches
- Wed Dec 13, 2017 8:45 pm
- Forum: Number Theory
- Topic: Yet divisibility...
- Replies: 6
- Views: 8213
Re: Yet divisibility...
This is an IMO $1994$ problem.Look up the problem in $AoPS$.
- Mon Dec 11, 2017 1:55 pm
- Forum: Higher Secondary Level
- Topic: A strange NUMBER THEORY Problem
- Replies: 4
- Views: 7237
Re: A strange NUMBER THEORY Problem
The $3rd$ number begets an answer of $-1$ which isn't a natural number.
- Fri Jul 07, 2017 1:08 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 45763
Re: Beginner's Marathon
Problem $26$
Given an acute angled triangle $\bigtriangleup ABC$.Inscribe in it a triangle $UVW$ of least possible perimeter.
Given an acute angled triangle $\bigtriangleup ABC$.Inscribe in it a triangle $UVW$ of least possible perimeter.
- Fri Jul 07, 2017 10:45 am
- Forum: Number Theory
- Topic: More primes and more primes!
- Replies: 1
- Views: 2540
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 ...
- Wed Jul 05, 2017 7:55 pm
- Forum: Number Theory
- Topic: More primes and more primes!
- Replies: 1
- Views: 2540
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.
- Tue Jul 04, 2017 7:46 pm
- Forum: Number Theory
- Topic: Infinite solutions
- Replies: 1
- Views: 2401
Infinite solutions
Find with proof every pair of ($a$,$b$) in general form such that $a+b^2$|$a^3+b^3$.
- Mon Jun 19, 2017 3:02 pm
- Forum: Geometry
- Topic: IMO 2009 SL(G-1)
- Replies: 1
- Views: 8734
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 $\angle BA...
- Thu Jun 15, 2017 2:44 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 45763
Re: Beginner's Marathon
What has been meant by 'after 2 hours 30 min'?
- Fri Jun 09, 2017 4:27 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 45763
Re: Beginner's Marathon
An easy problem:$\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.
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.
- Thu Jun 08, 2017 11:42 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 45763
Re: Beginner's Marathon
$\text{Problem 19}$ Let,the number of games played by a person $i$ be $g_i$.Therefore,the sum $g_1$+$g_2$+......+$g_{127}$ is even as each game is counted twice.We,assume that the number of people who played an odd numbered games is odd.In that case,if we eliminate their played games from the sum,we...