solve asap within 10 mins or else downvote Whether each of the following statements are true or false. Write TRUE or FALSE.(a) In the RSA algorithm with n = pq, the integers D and E are chosen so that the productDE = 1 (mod n).(b) If n = pq where p and q are distinct prime numbers (so p # q), then there exists a uniqueabelian group of order n.(c) If o e Sn, then the order of o is less than or equal to n.for EACH of these a, b, c, state true orfalse. No expalination needed

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 27E

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Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic group of order n. Prove that G has elements of order 12 but no element of order greater than 12. Find the number of distinct elements of G that have order 12.
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