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?

Guest 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!

:)

ilorty Aug 21, 2020

#4