## Search found 45 matches

### Re: Beginner's Marathon

Problem $26$
Given an acute angled triangle $\bigtriangleup ABC$.Inscribe in it a triangle $UVW$ of least possible perimeter.
Fri Jul 07, 2017 1:08 pm

Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 3616

### 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 ...
Fri Jul 07, 2017 10:45 am

Forum: Number Theory
Topic: More primes and more primes!
Replies: 1
Views: 234

### 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.
Wed Jul 05, 2017 7:55 pm

Forum: Number Theory
Topic: More primes and more primes!
Replies: 1
Views: 234

### Infinite solutions

Find with proof every pair of ($a$,$b$) in general form such that $a+b^2$|$a^3+b^3$.
Tue Jul 04, 2017 7:46 pm

Forum: Number Theory
Topic: Infinite solutions
Replies: 1
Views: 209

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 $\angle BA... Mon Jun 19, 2017 3:02 pm Forum: Geometry Topic: IMO 2009 SL(G-1) Replies: 1 Views: 216 ### Re: Beginner's Marathon What has been meant by 'after 2 hours 30 min'? Thu Jun 15, 2017 2:44 pm Forum: Junior Level Topic: Beginner's Marathon Replies: 68 Views: 3616 ### Re: Beginner's Marathon An easy problem:$\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. Fri Jun 09, 2017 4:27 pm Forum: Junior Level Topic: Beginner's Marathon Replies: 68 Views: 3616 ### 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... Thu Jun 08, 2017 11:42 pm Forum: Junior Level Topic: Beginner's Marathon Replies: 68 Views: 3616 ### Re: 2017 Regional no.9 Dhaka Check the parity of the equation and the rest should be clear. Mon Jun 05, 2017 2:31 pm Forum: Divisional Math Olympiad Topic: 2017 Regional no.9 Dhaka Replies: 9 Views: 480 ### Re: MPMS Problem Solving Marathon Simplier solution to problem$1$,I used this after getting to know what Wilson's Theorem is from dshasan's post.Let,$a$=$1$.$2$......$2k$.Telescope$a^2$as$1$.$2$....$2k$.($-2k$)....($-2$)($-1$).From the telescoping,it follows$a^2\equiv1$.$2$....$2k$($p-2k$)....($p-2$)($p-1$) (mod$p...
Mon Jun 05, 2017 2:09 pm

Forum: News / Announcements
Topic: MPMS Problem Solving Marathon
Replies: 8
Views: 594
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