Ernst Kummer tried in vain to prove Fermat's Last Theorem, and his method (similar to Fermat's own) broke down because not all rings have the "nice" property of unique factorization. Studying these unique factorization domains did not lead to a proof of Fermat's Last Theorem, but it did lead to the study of these:
a. Prime numbers
b. Algebraic numbers
c. Ideals
d. Ring generators
