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Let P be the set of 42nd roots of unity, and let Q be the set of 70th roots of unity. How many elements do P and Q have in common?

 

Let P be the set of 42nd roots of unity, and let Q be the set of 70th roots of unity. What is the smallest positive integer n for which all the elements in P and all the elements in Q are nth roots of unity?
 

 Aug 21, 2020
 #1
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0

1. P and Q have 28 elements in common.

 

2. The smallest n is 280.

 Aug 21, 2020
 #2
avatar+1042 
+4

I'll do number two for you, which should help you with number 1. If you are still confused, feel free to ask me.

 

2) Beneath all that ugly mathematician jargon lies a simple, beautiful, question: What is the LCM of 42 and 70? Solving this is simple, it gives us 210.

 

hint for number 1: If I told you should divide 210 into something, what would you do?

 

If you need more  help, feel free to ask. Also, if my answer is wrong, please tell me, so I can correct it!

 

:)

 Aug 21, 2020
 #4
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0

Thank you so much ilorty!

 

I got 14 for the first part, is that correct?

littlemixfan  Aug 22, 2020
 #5
avatar+1042 
+3

Remember, 0 also works!

ilorty  Aug 22, 2020

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