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nuclislath7957
nuclislath7957
14.04.2020 • 
Mathematics

3) (40 pts.--10 pts. each) Determine an inverse of a modulo m for the following pair of relatively prime integers: a=2, m=13 Show each step as you follow the method given in Rosen 7th edition page 276 example 2 and also given in Example 3.7.1 p. 167 of the Course Notes. Beside your solution in part a), identify two other inverses of 2 mod 13. Hint: All of these inverses are congruent to each other mod 13. One of your answers for part a) or part b) may be a non-negative integer <13; if so, use that inverse for this problem. If not, identify a non-negative inverse of 2 modulo 13 that is <13 and use it for solving this problem. Use the non-negative inverse of 2 modulo 13 that is <13 to solve the following congruence: 2x≡8(mod13) Show the steps used to determine your solution. Determine if the congruence 2x ≡ 13(mod 8) has a solution for x. If there is a solution, determine a solution. If there is no solution, explain why not.

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