Make a lattice diagram of Z modulo 7 excluding 0 under the binary operation of multiplication
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Make a lattice diagram of Z modulo 7 excluding 0 under the binary operation of multiplication
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- In this exercise set, all variables are integers. 2. Follow the instructions in Exercise for the congruence classes modulo . 1. List the distinct congruence classes modulo , exhibiting at least three elements in each class.30. Prove that any positive integer is congruent to its units digit modulo .In this exercise set, all variables are integers. 1. List the distinct congruence classes modulo , exhibiting at least three elements in each class.
- a. Excluding the identity cipher, how many different translation ciphers are there using an alphabet of n "letters"? b. Excluding the identity cipher, how many different affine ciphers are there using an alphabet of n "letters," where n is a prime?Let n be appositive integer, n1. Prove by induction that the set of transpositions (1,2),(1,3),...,(1,n) generates the entire group Sn.Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .