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lime · 2008 November 3rd, 07:01 PM

Consider group Z15 under addition. Then element x=5 satisfies given conditions. Indeed:

5^3=3*5=15=0
5^5=5*5=25=10
5^9=9*5=45=0

Then

x^13=65=5

Element 5 generates subgroup of order 3.

2008 November 3rd, 07:01 PM	#5 (permalink)
lime Glutton! Join Date: Nov 2007 Location: Russia Posts: 949	Consider group Z15 under addition. Then element x=5 satisfies given conditions. Indeed: 5^3=35=15=0 5^5=55=25=10 5^9=9*5=45=0 Then x^13=65=5 Element 5 generates subgroup of order 3.