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