Determine the inverse modulo m of some (relatively prime) integer n. Thus, find the inverse of 4 mod 27 (i.e. an integer c such that 4c = 1 (mod 27). (a) Perform Euclid's algorithm on 4 and 27. 27 = 6( + (1) +1 (Note your answers on the second row should match the ones on the first row.) Therefore, god(4, 27) = 1 and 4 and 27 are relatively prime. (b) Run Euclid's algorithm backwards to write 1 = 27s + 4t for suitable integers s, t. (c) From the equation 27s + 4t =1 (mod 27), the multiple of 27 becomes zero (because we are considering congruence) and so we get 4t = 1 (mod 27). Hence the multiplicative inverse of 4 mod 27 is