Find the modular inverse of 27, modulo 29. Express your answer as an integer from 0 to 28, inclusive.
\(27A=1(mod29)\\ 27A=-29N+1\\ 29N+27A=1\\~\\ 29=1(27)+2\\ 27=13(2)+1\\ 27-13(2)=1\\ 27-13(29-1(27))=1\\ 27-13(29)+13(27)=1\\ 14(27)-13(29)=1\\ 27*14=1(mod29)\\ \)
So the modular inverse of 27 mod 29 is 14
