Happy new year to everybody. Ok, see if you like this problem as much as I do:

Let and suppose that Prove that if then

Source: Alex Lupas

Note: The problem has a simple generalization.

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- Dec 31st 2008, 03:21 PMNonCommAlgAn upper bound for roots of certain polynomials
Happy new year to everybody. Ok, see if you like this problem as much as I do:

Let and suppose that Prove that if then

__Source__: Alex Lupas

__Note__: The problem has a simple generalization. - Feb 4th 2009, 07:02 AMDeMath
- Feb 7th 2009, 12:51 PMNonCommAlg
- Feb 14th 2009, 10:57 AMDeMath
Also we can not difficult to prove your problem by methods of complex analysis, using Rouche's theorem.

P.S. I would be interested to see your proof. - Feb 14th 2009, 03:11 PMNonCommAlg
in general:

let and such that: suppose also that and:

then all roots of lie in the disc to prove this, suppose that and first note that if then:

now we have: therefore: but by and our assumption:

contradiction!