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Fermat’s Last Theorem (FLT) states that there is no natural number set {a, b, c, n} which satisfies an+bn=cn or an=cn-bn when n ≥ 3. In this thesis, we related LHS and RHS of an=cn-bn to the constant terms of two monic polymials xn-an and xn-(cn-bn). By doing so, we could inspect whether these two polynomials can be identical when n ≥ 3, i.e., xn-an=xn-(cn-bn), which satisfies an=cn-bn. By inspecting the properties of two polynomials such as factoring, root structures and graphs, we found that xn-an and xn-(cn-bn) can’t be identical when n ≥ 3, except when trivial cases.
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