## Search found 31 matches

### Re: IMO $2017$ P$1$

Please someone post a solution...
Fri Sep 15, 2017 3:11 am

Forum: International Mathematical Olympiad (IMO)
Topic: IMO $2017$ P$1$
Replies: 2
Views: 238

### Re: Yet divisibility...

Wed Sep 06, 2017 6:04 pm

Forum: Number Theory
Topic: Yet divisibility...
Replies: 1
Views: 147

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

Someone?
Wed Sep 06, 2017 6:02 pm

Forum: Algebra
Topic: a+b+c>=1/a+1/b+1/c
Replies: 1
Views: 132

### Re: Sequence and divisibility

Thanks tanmoy.
Wed Sep 06, 2017 5:52 pm

Forum: Algebra
Topic: Sequence and divisibility
Replies: 2
Views: 163

### 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 $a_k(a_1 - 1).$
Thu Aug 24, 2017 10:27 pm

Forum: Algebra
Topic: Sequence and divisibility
Replies: 2
Views: 163

### Re: Double inequality

Yes sMMamum, it was obviously an error.
Very good and clear solution.
Thanks!!
Thu Aug 24, 2017 10:22 pm

Forum: Algebra
Topic: Double inequality
Replies: 3
Views: 158

### Re: Double inequality

Someone?
Sat Aug 19, 2017 11:10 pm

Forum: Algebra
Topic: Double inequality
Replies: 3
Views: 158

### Re: Equality and square

Thanks Antonu!
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...
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: 121

### Re: IMO $2017$ P$1$

Anyone??
Fri Aug 04, 2017 1:25 pm

Forum: International Mathematical Olympiad (IMO)
Topic: IMO $2017$ P$1$
Replies: 2
Views: 238
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