MHB Group Elements of Z24: Find the Order

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The discussion focuses on determining the order of each element in the additive group Z24, which consists of integers modulo 24. Participants clarify that Z24 has 23 non-zero members, and the order of an element is defined as the smallest integer n such that n times the element equals zero modulo 24. For example, the element 6 has an order of 4 since adding it four times results in 24, which is equivalent to 0 in this group. Additionally, it is noted that elements like 5, which are not divisors of 24, have an infinite order. Understanding these concepts is crucial for accurately calculating the orders of all elements in Z24.
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Determine the order of every element of Z24
 
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kindly infrom what you have tried and where you are facing problems
 
Do you understand that "z24" is the additive group of integers modulo 24? That has 23 non-zero members so you will need to give 23 answers. Do you further understand that the "order" of a member, a, of a group is the integer "n" such that na= 0 where "na" means a added to itself n times. For example 6+ 6+ 6+ 6= 24= 0 (mod 24) so 6 has order 4. No multiple of 5 will be 24 so the order of 5 (and any number that is not a divisor of 24) is "infinity".
 

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