ahw8 - MAT 312/AMS 351 – Fall 2010 Homework 8 1. In p. 56...

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Unformatted text preview: MAT 312/AMS 351 – Fall 2010 Homework 8 1. In p. 56 problem (6), check that the first block (13615) decodes to 40 = “O”. You may do this as follows: first check that the multiplicative inverse of 121 modulo ϕ(23711) = 23400 is 3481. Show your work. Then use a calculator to compute 136153481 modulo 23711 by calculating the following powers of 13615 mod 23711: 2, 4, 8, 10, 20, 40, 80, 100, 200, 400, 800, 1000, 2000, 3000, 3400, 3480, 3481. 2. Decode the second block (19917). Show your work! 3. page 76 problem (1). 4. page 76 problem (2). 5. A transposition is a cycle of length 2. Check the (elementary) proof on p. 82 that every cycle is a product of transpositions. Then prove that every permutation is a product of transpositions. 6. Explain why that product is not unique. 7. Write the permutation π= 12345678 46187523 as a product of transpositions. 1 ...
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