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Re: IMO $2017$ P$1$

Please someone post a solution... :( :(
by Katy729
Fri Sep 15, 2017 3:11 am
 
Forum: International Mathematical Olympiad (IMO)
Topic: IMO $2017$ P$1$
Replies: 2
Views: 240

Re: Yet divisibility...

Please a solution... :(
by Katy729
Wed Sep 06, 2017 6:04 pm
 
Forum: Number Theory
Topic: Yet divisibility...
Replies: 1
Views: 148

Re: a+b+c>=1/a+1/b+1/c

Someone? :(
by Katy729
Wed Sep 06, 2017 6:02 pm
 
Forum: Algebra
Topic: a+b+c>=1/a+1/b+1/c
Replies: 1
Views: 133

Re: Sequence and divisibility

Thanks tanmoy. :)
by Katy729
Wed Sep 06, 2017 5:52 pm
 
Forum: Algebra
Topic: Sequence and divisibility
Replies: 2
Views: 164

Sequence and divisibility

Let $ n$ be a positive integer and let $ a_1,a_2,a_3,\ldots,a_k$ $ ( k\ge 2)$ be distinct integers in the set $ { 1,2,\ldots,n}$ such that $ n$ divides $ a_i(a_{i + 1} - 1)$ for $ i = 1,2,\ldots,k - 1$. Prove that $ n$ does not divide $ a_k(a_1 - 1).$
by Katy729
Thu Aug 24, 2017 10:27 pm
 
Forum: Algebra
Topic: Sequence and divisibility
Replies: 2
Views: 164

Re: Double inequality

Yes sMMamum, it was obviously an error.
Very good and clear solution.
Thanks!! :)
by Katy729
Thu Aug 24, 2017 10:22 pm
 
Forum: Algebra
Topic: Double inequality
Replies: 3
Views: 159

Re: Double inequality

Someone? :(
by Katy729
Sat Aug 19, 2017 11:10 pm
 
Forum: Algebra
Topic: Double inequality
Replies: 3
Views: 159

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: 172

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: 122

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: 2
Views: 240
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