Question

The number of element of order 5 in the group z15 * z5 is.
1. 24
2. 4
3. 16
4. 8

Answer 1

Answer:

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Answer 2

number of elements of order5 in z15*z5 with property that o(a, b) =lcm(o(a),o(b))=5,given therefore possibility of o(a) =5 and o(b) =1,5 or o(b) =5 and o(a)is 1,5 so for choice a is (3,6,9,12) and five choices for b therefore 20 elements and o(a) =1 and o(b) =5 there are 1 choice for a and four choice for b so 1×4=4 so total number of elements 20+4=24