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




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 counterexample to the case k, you can easily make it into a counterexample to the case k1 . (By obliterating the largest integer.)
So this is really induction in the style of Fermat's method of infinite descent.
OK?
Steve



