Search found 550 matches
- Thu Jan 26, 2012 7:35 am
- Forum: Number Theory
- Topic: Determinining the floor
- Replies: 5
- Views: 3737
Re: Determinining the floor
I don't understand.....It's a problem from the national math olympiad of Russia,1995.I myself solved it and checked the official solution. I would be greatful if you send me a private message involving your check.
- Thu Jan 26, 2012 7:29 am
- Forum: Number Theory
- Topic: Sum Challenge
- Replies: 6
- Views: 4259
Re: Sum Challenge
Have you found errors?But I checked my use of Vinogradov's......now Iam also confused....
- Thu Jan 26, 2012 7:20 am
- Forum: Number Theory
- Topic: Polynomials
- Replies: 1
- Views: 1895
Polynomials
The polynomial $P(x)$ satisfies the following condition,
$P(2x^{2}-1) =( P(x)^{2}/2)-1$
What is the difference between the highest and lowest value of $P(x)$? Note that more than one such polynomials exists.
$P(2x^{2}-1) =( P(x)^{2}/2)-1$
What is the difference between the highest and lowest value of $P(x)$? Note that more than one such polynomials exists.
- Thu Jan 26, 2012 7:09 am
- Forum: Number Theory
- Topic: Sequences of interest
- Replies: 5
- Views: 3551
Sequences of interest
Separate the natural numbers into two sequences , namely $F(n)$ & $G(n)$ such that $F(n)$ contains the squares and $G(n)$ contains the non squares, i.e., $F(n)=1,4,9,16,25,36,49,....$ & $G(n)=2,3,5,6,7,8,10,........$ Surely $F(n)=n^{2}$.Now is there any formula to calculate $G(n)$?If there is ,then...
- Wed Jan 25, 2012 12:44 am
- Forum: Algebra
- Topic: Inequality about Angle Bisectors [self-made]
- Replies: 4
- Views: 3167
Re: Inequality about Angle Bisectors [self-made]
Have you given it in Pms before?
- Wed Jan 25, 2012 12:40 am
- Forum: National Math Olympiad (BdMO)
- Topic: SUMMATION
- Replies: 2
- Views: 2639
Re: SUMMATION
I solved it with induction
- Wed Jan 25, 2012 12:21 am
- Forum: Number Theory
- Topic: Sum Challenge
- Replies: 6
- Views: 4259
Re: Sum Challenge
ADB! you should try vinogradov's theoremPhlembac Adib Hasan wrote:বড় সংখ্যার জন্য কাজ করতেসে না। ক্যালকুলেশনেই ভুল করলাম কিনা
- Wed Jan 25, 2012 12:12 am
- Forum: Number Theory
- Topic: Determinining the floor
- Replies: 5
- Views: 3737
Re: Determinining the floor
Sorry.The recurrence holds for $n=0$ too.And yes,$[a_{1}]=1995$.And i put [] before and after $a_{n}^{2}+1$ not to indicate floor, but to indicate bracket.
- Wed Jan 25, 2012 12:08 am
- Forum: Number Theory
- Topic: Rational solution
- Replies: 6
- Views: 3795
Re: Rational solution
Yes, my solution says so.But i wanna match it with you two.Please post the solution.
- Sun Jan 22, 2012 6:22 am
- Forum: Number Theory
- Topic: Rational solution
- Replies: 6
- Views: 3795
Rational solution
Is there a positive integer $n$ such that the sum of the square roots of the adjacent integers of$n$ is rational.