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 cs-312:hw3 [2015/01/12 08:36]ringger [Exercises] cs-312:hw3 [2015/01/12 08:37]ringger Both sides previous revision Previous revision 2015/01/12 08:37 ringger 2015/01/12 08:36 ringger 2015/01/12 08:36 ringger [Exercises] 2014/12/31 15:54 ringger created Next revision Previous revision 2015/01/12 08:37 ringger 2015/01/12 08:36 ringger 2015/01/12 08:36 ringger [Exercises] 2014/12/31 15:54 ringger created Line 5: Line 5: - '''​Part ​1:'''​ + === Question ​1 === - * 1.9 in the textbook (be sure to complete both proofs! -- each is worth 3 points) + 1.9 in the textbook (be sure to complete both proofs! -- each is worth 3 points) - ** "​justify"​ means prove using a two column proof: one column for statements and one column for reasons. + * "​justify"​ means prove using a two column proof: one column for statements and one column for reasons. - ** (proof #1 completed in class) + - '''​Part ​2:'''​ + === Question ​2 === - * 1.18 in the textbook + 1.18 in the textbook - '''​Part ​3:'''​ + === Question ​3 === - * 1.20 in the textbook (four sub-problems -- each is worth 3 points) + 1.20 in the textbook (four sub-problems -- each is worth 3 points) - ** Use the Extended Euclid method on two of the sub-problems + * Use the Extended Euclid method on two of the sub-problems - ** Any method (including Extended Euclid) is welcome for the other two sub-problems + * Any method (including Extended Euclid) is welcome for the other two sub-problems - + * If you get a negative result for the multiplicative inverse, then add the modulus until you obtain a positive value between 0 and the modulus (exclusive of 0 and the modulus). - If you get a negative result for the multiplicative inverse, then add the modulus until you obtain a positive value between 0 and the modulus (exclusive of 0 and the modulus). + In order to be successful on the problems using the Extended Euclid algorithm, please be sure to consult the posted example. ​ It is a walk-through of the recursive algorithm: ​ [http://​faculty.cs.byu.edu/​~ringger/​CS312/​readings/​ExtendedEuclidExample.pdf Worked Example] In order to be successful on the problems using the Extended Euclid algorithm, please be sure to consult the posted example. ​ It is a walk-through of the recursive algorithm: ​ [http://​faculty.cs.byu.edu/​~ringger/​CS312/​readings/​ExtendedEuclidExample.pdf Worked Example] 