In this research simple proofs of Fermat’s last theorem of last theorem are proposed. The proofs presented do not require any Galois representation or concepts of elliptic curves. In the first proof a most general algebraic coordinate representation of Pythagorean integer triples is proposed. The triples will be powered to some general degree n to enable derivation of the proof. In the second proof method a general algebraic formula containing all the Pythagorean triples is proposed. The… Expand