5 Modular Practice (a) Calculate 72316 mod 7. (b) Solve the following system for c: 3x = 4+y 2(x - 1) = 2y (mod 5) (mod 5) (c) If it exists, find the multiplicative inverse of 31 mod 23 and 23 mod 31. (d) Let n, x be positive integers. Prove that x has a multiplicative inverse modulo n if and only if ged(n,x) = 1. (Hint: Remember an iff needs to be proven both directions. The ged cannot be O or negative.)