Galois representations were used to show that every elliptical curve has a modular form proving a special case of the Taniyama-Shimura conjecture, which implies this statement regarding the solvability of a Diophantine equation involving the addition of a to the n and b to the n to yield c to the n. Richard Taylor and Andrew Wiles gave the proof of, for 10 points, what theorem, whose solution did not fit the margin's of its namesake French mathematician's notebook.
Ernst Kummer's work on this theorem to the development of the theory of ideals, and the smaller of the irregular pair which satisfies Vandiver's criteria also satisfies this statement. Galois representations were used to show that every elliptical curve has a modular form proving a special case of the Taniyama-Shimura conjecture, which implies this statement regarding the solvability of a Diophantine equation involving the addition of a to the n and b to the n to yield c to the n. Richard Taylor and Andrew Wiles gave the proof of, for 10 points, what theorem, whose solution did not fit the margin's of its namesake French mathematician's notebook.
Ernst Kummer's work on this theorem to the development of the theory of ideals, and the smaller of the irregular pair which satisfies Vandiver's criteria also satisfies this statement.
{Fermat's last} theorem [do not accept “{Fermat's little theorem}”]