## Search found 48 matches

Sat Dec 16, 2017 7:37 pm
Forum: Number Theory
Topic: Prime numbers
Replies: 3
Views: 146

### Re: Prime numbers

$n$=$2,5,7$.
Wed Dec 13, 2017 8:45 pm
Forum: Number Theory
Topic: Yet divisibility...
Replies: 6
Views: 478

### 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: 3
Views: 230

### 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: 4024

### 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 10:45 am
Forum: Number Theory
Topic: More primes and more primes!
Replies: 1
Views: 282

### 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: 282

### 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: 242

### 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: 257