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If a and a2 both are generator of a cyclic group, then the order of the group gcd(2, n) = 1⇒ n = odd positive integer > 1
  • a)
    cannot be prime
  • b)
    only prime
  • c)
    any odd positive integer
  • d)
    only even integer
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If a anda2 both are generator of a cyclic group, then theorder of the ...
This statement is not necessarily true.

If a and b are both generators of a cyclic group, then the order of the group is equal to the order of any generator. The order of a generator is the smallest positive integer k such that a^k = e (the identity element).

In this case, if a and b are both generators of the cyclic group, then their orders should be equal. If the order of a is gcd(2, n), then the order of b should also be gcd(2, n).

However, it is not necessary that gcd(2, n) = 1. The greatest common divisor (gcd) of 2 and n could be any positive integer greater than 1. Therefore, the statement is not necessarily true.
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If a anda2 both are generator of a cyclic group, then theorder of the group gcd(2, n) = 1⇒ n = odd positive integer > 1a)cannot be primeb)only primec)any odd positive integerd)only even integerCorrect answer is option 'C'. Can you explain this answer?
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