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Re: Goldbach Conjecture
Posted:
Sep 17, 2000 2:51 AM
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On 17 Sep 2000, Daniel McLaury wrote:
> I don't think that Euler would have been fooled by something
> as simple as x^2 + x + 41. After all, it is obvious that f(41)
> is 41*43. He may have given this as an example of why not to
> rely on anecdotal evidence. One of my favorites is the polynomial
> (x-1)(x-2)(x-3)*...(x-n), multiplied out so that its form is not
> so obvious. Then the prof/teacher says, f(1) = 0, f(2) = 0, ...
> so therefore f(x) must always equal 0. Half the students are
> convinced, and then the teacher takes f(n+1) = n!, which is
> _very_ far from being 0.
A silly example: the "identity" (1+2+3+...+n)! = 1!3!5!...(2n-1)!
which is true for n = 0, 1, 2, 3, and 4, but false for all larger
values of n. Not in the same league with Euler's x^2+x+41 of course.
--
"Any clod can have the facts, but having opinions is an art."--McCabe
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