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Does there exists integers a, b and c such that \(a^{100}+b^{100}=c^{100} \)?

 Jun 26, 2020
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Fermat's Last Theorem (which was proven by Andrew Wiles) states that there are no three posiitve integers greater than 2

for which the equation an + bn = cn is true.

 

The restriction that the values must be positive disallows situations such as this:

  if a = -1, b = 1, and c = 0, then (-1)3 + (1)3 = (0)3  [which is true].

 

However, in the expression a100 + b100  =  c100, because of the even exponents, if you could find any negative value that could be used, its corresponding positive value could also be used; but this is not allowed under Fermat's Last Theorem.

 Jun 26, 2020

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