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

Guest Jun 26, 2020

#1**+1 **

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 a^{n} + b^{n} = c^{n} 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 a^{100} + b^{100} = c^{100}, 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.

geno3141 Jun 26, 2020