Search found 47 matches
- Thu Aug 24, 2017 10:27 pm
- Forum: Algebra
- Topic: Sequence and divisibility
- Replies: 2
- Views: 8132
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 10:22 pm
- Forum: Algebra
- Topic: Double inequality
- Replies: 3
- Views: 8760
Re: Double inequality
Yes sMMamum, it was obviously an error.
Very good and clear solution.
Thanks!!
Very good and clear solution.
Thanks!!
- Sat Aug 19, 2017 11:10 pm
- Forum: Algebra
- Topic: Double inequality
- Replies: 3
- Views: 8760
Re: Double inequality
Someone?
- Sat Aug 19, 2017 11:09 pm
- Forum: Number Theory
- Topic: Equality and square
- Replies: 2
- Views: 5569
Re: Equality and square
Thanks Antonu!
- 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: 6057
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 1:25 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO $2017$ P$1$
- Replies: 4
- Views: 8762
Re: IMO $2017$ P$1$
Anyone??
- Fri Aug 04, 2017 1:24 pm
- Forum: Number Theory
- Topic: Equality and square
- Replies: 2
- Views: 5569
Equality and square
Determine all pairs $(a, b)$ of integers such that
$1+2^{a}+2^{2b+1}= b^{2}$
$1+2^{a}+2^{2b+1}= b^{2}$
- Fri Aug 04, 2017 1:21 pm
- Forum: Algebra
- Topic: Double inequality
- Replies: 3
- Views: 8760
Double inequality
Prove that $0\le bc+ca+ab-2abc\le{7\over27}$, where $x,y$ and $z$ are non-negative real numbers satisfying $a+b+c=1$
- Sat Jul 01, 2017 3:46 pm
- Forum: Algebra
- Topic: Good inequality..
- Replies: 2
- Views: 7971
Re: Good inequality..
good and clear solution. Thanks!
- Sat Jul 01, 2017 3:44 pm
- Forum: Number Theory
- Topic: Beautifull divisibility
- Replies: 1
- Views: 2455
Beautifull divisibility
Determine all pairs $(a,b)$ of positive integers such that $a^{2}b+a+b$ is divisible by $ab^{2}+b+7$