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Re: Double inequality

Someone? :(
by Katy729
Sat Aug 19, 2017 11:10 pm
 
Forum: Algebra
Topic: Double inequality
Replies: 1
Views: 67

Re: Equality and square

Thanks Antonu! :)
by Katy729
Sat Aug 19, 2017 11:09 pm
 
Forum: Number Theory
Topic: Equality and square
Replies: 2
Views: 103

Imo 3 2017 (the most cute and difficult... xd)

A hunter and an invisible rabbit play a game in the Euclidean plane. The rabbit's starting point, $A_0,$ and the hunter's starting point, $B_0$ are the same. After $n-1$ rounds of the game, the rabbit is at point $A_{n-1}$ and the hunter is at point $B_{n-1}.$ In the $n^{\text{th}}$ round of the gam...
by Katy729
Fri Aug 04, 2017 1:31 pm
 
Forum: International Mathematical Olympiad (IMO)
Topic: Imo 3 2017 (the most cute and difficult... xd)
Replies: 0
Views: 70

Re: IMO $2017$ P$1$

Anyone?? :(
by Katy729
Fri Aug 04, 2017 1:25 pm
 
Forum: International Mathematical Olympiad (IMO)
Topic: IMO $2017$ P$1$
Replies: 1
Views: 167

Equality and square

Determine all pairs $(a, b)$ of integers such that
$1+2^{a}+2^{2b+1}= b^{2}$
by Katy729
Fri Aug 04, 2017 1:24 pm
 
Forum: Number Theory
Topic: Equality and square
Replies: 2
Views: 103

Double inequality

Prove that $0\le bc+ca+ab-2abc\le{7\over27}$, where $x,y$ and $z$ are non-negative real numbers satisfying $a+b+c=1$
by Katy729
Fri Aug 04, 2017 1:21 pm
 
Forum: Algebra
Topic: Double inequality
Replies: 1
Views: 67

Re: Good inequality..

good and clear solution. Thanks! :)
by Katy729
Sat Jul 01, 2017 3:46 pm
 
Forum: Algebra
Topic: Good inequality..
Replies: 2
Views: 165

Beautifull divisibility

Determine all pairs $(a,b)$ of positive integers such that $a^{2}b+a+b$ is divisible by $ab^{2}+b+7$
by Katy729
Sat Jul 01, 2017 3:44 pm
 
Forum: Number Theory
Topic: Beautifull divisibility
Replies: 1
Views: 183

no solution (a,b)

Prove that there is no pair $(a,b)$ of integers such that
$a^2=b^7+7$
by Katy729
Sat Jul 01, 2017 3:40 pm
 
Forum: Number Theory
Topic: no solution (a,b)
Replies: 0
Views: 112

Yet divisibility...

Determine all ordered pairs $(a,b)$ of positive integers for which $\dfrac{b^3+1}{ab-1}$ is an integer.
by Katy729
Sat Jul 01, 2017 3:35 pm
 
Forum: Number Theory
Topic: Yet divisibility...
Replies: 0
Views: 95
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