1.9. Compute x as far as possible without a calculator. Where appropriate, make use of a smart decomposition of the exponent as shown in the example in Sect. 1.4.1: 1. x = 32 mod 13 2. x = 72 mod 13 3. x = 310 mod 13 4. x = 7100 mod 13 5. 7^x = 11 mod 13 The last problem is called a discrete logarithm and points to a hard problem which we discuss in Chap. 8. The security of many public-key schemes is based on the hardness of solving the discrete logarithm for large numbers, e.g., with more than 1000 bits.