Find all elements x1,x2,x3,... in Z77 such that each 〈xi〉 is a proper subgroup of Z77. Enter your answer as a comma-separated list.

blogswput

blogswput

Answered question

2022-09-09

Find all elements x 1 , x 2 , x 3 , . . .</mo in Z 77 such that each x i is a proper subgroup of Z 77 . Enter your answer as a comma-separated list.

Answer & Explanation

scrapbymarieix

scrapbymarieix

Beginner2022-09-10Added 15 answers

Remember that,
x i ¯ is a generator for the group Z 77 if and only if gcd ( x i , 77 ) = 1
So, < x i > is a proper subgroup if and only if C is divisible by either 7 or 11.
So the answers are basically all the multiples of 7 and 11.

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