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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
0

1. P and Q have 28 elements in common.

2. The smallest n is 280.

Aug 21, 2020
#2
+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
0

Thank you so much ilorty!

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

littlemixfan  Aug 22, 2020
#5
+3

Remember, 0 also works!

ilorty  Aug 22, 2020