This is Wiles’ lifting theorem or modularity lifting theorema major and revolutionary accomplishment at the time. The so-called “first case” of the theorem is for exponents which are relatively prime to, and and was considered by Wieferich. Note that is ruled out by, being relatively prime, and that if divides two of,then it also divides the third, by equation 8.
If you would be a research level mathematician with a sound knowledge of algebra, algebraic geometry. I don’t know who you are and what you know already. On June 23,, Andrew Wiles wrote on a blackboard, before. When the ten-year-old Andrew Wiles read about it in his local Cambridge At the age of ten he began to attempt to prove Fermat’s last theorem.
