"Adam Beneschan" <adam@[EMAIL PROTECTED]
> wrote in
news:1157578434.483014.313500@[EMAIL PROTECTED]
> Rob Morris wrote:
>
>
>> > 'A sum, proved impossible by the theorem, appears in an episode of
>> > The Simpsons, "Treehouse of Horror VI". In the three-dimensional
>> > world in "Homer3", the equation 1782 ^ 2 + 1841 ^ 2 = 1922 ^ 2 is
>> > visible, just as the dimension begins to collapse.'
>>
>> I believe it's:
>> 1782^12 + 1841^12 = 1922^12
>> - the point being that if you do 1782^12 + 1841^12 on your calculator
>> then take the twelfth root, you'll probably get 1922. However this
>> is just due to precision lost in the calculation. Wikipedia says the
>> left-hand side is equal to
>> 2,541,210,258,614,589,176,288,669,958,142,428,526,657
>> while the right hand side is:
>> 2,541,210,259,314,801,410,819,278,649,643,651,567,616
>
> Also, just to nitpick further, although it's true that the equation
> would be proven impossible by the theorem, that particular equation
> would have been known to be impossible for a very long time even
> without doing the computation. According to Wikipedia, Fermat himself
> had already proven that his theorem was true for n=4, and that would
> automatically make the above equation impossible since it is
> equivalent to (1782^3)^4 + (1841^3)^4 = (1922^3)^4. (Similarly, FLT
> has been known for a very long time to be true for n=3.)
>
> -- Adam
>
>
It is pretty late but isn't any odd number times any odd number always
an odd number(1841^any will be odd) and evens always produce
evens(1782^any)? And an even plus an odd always odd?
So 1782^x + 1841^x must be odd but 1922^x cannot be.
OB
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