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Home » Olympiad Section » Inequalities » Inequalities Unsolved Problems
 
general form of the old ineq
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romano
Riemann Hypothesis
Riemann Hypothesis

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#1
general form of the old ineq
Let t \geq 0 , x_n = \frac{1+t+t^2+..+t^n}{n+1} .
Prove that : ^{n-1}\sqrt{x_{n-1}} \leq ^n\sqrt{x_n} for all n \geq 1
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PostPosted: Sun Jan 30, 2005 8:19 am  Back to top 
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Birch & Swinnerton Dyer
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#2
It doesn't hold for n=1;

1\leq \frac {1+t}{2} is not generally true. I think we at least need t\geq 1.

PostPosted: Sun Jan 30, 2005 10:13 pm  Back to top 
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Myth
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#3
No we no need it, since inequalities for t and 1/t are the same Wink
Forget about n=1 Smile
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PostPosted: Sun Jan 30, 2005 10:48 pm  Back to top 
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romano
Riemann Hypothesis
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#4
Anybody , let's try to solve it !
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PostPosted: Mon Jan 31, 2005 8:21 am  Back to top 
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zhaobin
Navier-Stokes Equations
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#5
Myth wrote:
No we no need it, since inequalities for t and 1/t are the same Wink
Forget about n=1 Smile

I don't think it is the same.please think about it again. Smile

PostPosted: Mon Jan 31, 2005 8:41 am  Back to top 
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Myth
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#6
No, I am right Wink
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PostPosted: Mon Jan 31, 2005 8:43 am  Back to top 
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zhaobin
Navier-Stokes Equations
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#7
yes I'm sorry

PostPosted: Mon Jan 31, 2005 8:46 am  Back to top 
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romano
Riemann Hypothesis
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#8
For more understoodable explanation : We need to show that :
x_1 \leq \sqrt{x_2} \leq ^3\sqrt{x_3} \leq ^4{x_4} \leq ....
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PostPosted: Mon Jan 31, 2005 8:50 am  Back to top 
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zhaobin
Navier-Stokes Equations
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#9
assume t>1 can we let f(t)=\frac{(t^{n+1}-1)^{n-1}(t-1)}{(t^{n}-1)^n}
can we prove that f'(t)>0?

PostPosted: Mon Jan 31, 2005 11:28 am  Back to top 
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romano
Riemann Hypothesis
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#10
Ican't prove f'(t) > 0
How can you do with 0 < t < 1
In short , this problem is still unsolved ! Sad
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PostPosted: Tue Feb 01, 2005 8:40 am  Back to top 
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