( 1 point) The goal of this exercise is to practice finding the inverse modulo m of some (relatively prime) integer n. We will find the inverse of 9 modulo 58 , i.e., an integer c such that 9c1 (mod 58 ). First we perform the Euclidean algorithm on 9 and 58 : 58=6 =2+1 [Note your answers on the second row should match the ones on the first row.] Thus gcd(9,58)=1, i.e., 9 and 58 are relatively prime. Now we run the Euclidean algorithm backwards to write 1=58s+9t for suitable integers s,t. s= t= when we look at the equation 58s+9t1(mod58), the multiple of 58 becomes zero and so we get 9t1(mod58). Hence the multiplicative inverse of 9 modulo 58 is