Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Inequalities: a problem
Replies: 10   Last Post: Jul 12, 1996 9:56 AM

 Messages: [ Previous | Next ]
 Stephen.Donnelly Posts: 14 Registered: 12/12/04
Re: Inequalities: a problem
Posted: Jul 10, 1996 5:31 AM

In fact I think it can be generalised to any number k
of variables:

FACT:
Let a_1 .. a_k be distinct integers.
Then \sum [a_i - a_(i+1)]^2 >= 4k - 6 .

You can prove it by induction on k now.
The case k=2 is clear.
Then if there is a counter-example to the case k,
you can easily make it into a counter-example to
the case k-1 . (By obliterating the largest integer.)

So this is really induction in the style of Fermat's
method of infinite descent.

OK?

Steve

Date Subject Author
7/9/96 francis d'costa
7/10/96 Lukas Geyer
7/10/96 CDJ
7/10/96 Hauke Reddmann
7/10/96 Stephen.Donnelly
7/10/96 Rene Bos
7/12/96 Chris Thompson
7/10/96 CDJ
7/10/96 David Kastrup
7/12/96 francis d'costa
7/10/96 Stephen.Donnelly