10.) Consider (Zn; n), the set Zn with mod n
multiplication.
i. Argue that if neither a nor b has any common divisors greater
than 1
with n then neither does ab. [Equivalently gcd(a; n) = 1,
etc.]
ii. Argue that if a does not have any common divisors greater than
1
with n, then [a]n has a multiplicative inverse in Zn.
iii. Argue that (i) and (ii) imply that the set of elements
f[a]n 2 Znjgcd(a; n) = 1g with mod n multiplication is a
group.
Homework Answers
![(ii) Suppose ged (and=1 u, u E Then 7 a u the = 1 5 [aut no] = [1 | [au] + [no] [!] [a] [u] + [o ] [a] [u] [1] [1] V Hence, [](http://img.homeworklib.com/questions/fed1f3c0-e017-11ea-8cfb-d75e5ab90b2c.png?x-oss-process=image/resize,w_560)
![holds ie T Associativity clearly [a] [b] ) [c] [a] ( [b] [c]) Now [IJ E S ged (lino = 1 [a] [ - [a. l] =[a + [a] GS [I] is id](http://img.homeworklib.com/questions/ff55fdd0-e017-11ea-94b1-779ad282dc5e.png?x-oss-process=image/resize,w_560)
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10.) Consider (Zn; n), the set Zn with mod n
multiplication.
i. Argue that if neither...
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