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Need help on number theory II-A

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Need help on number theory II-A
by Kevin Song - Saturday, April 24, 2021, 7:56 PM

Hello, I don't know how to do 8.23,8.24 or 8.25a.


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Re: Need help on number theory II-A
by Areteem Professor - Monday, April 26, 2021, 11:32 AM

Hi Kevin, here are some hints:

For 8.23: The question started at the end of class was to show that a*b*c was always divisible by 60 for a Pythagorean triple (a,b,c). Therefore, we know that the M in 8.23 is a multiple of 60. Think about some common Pythagorean triples from here.

For 8.24, review what was done in class for 8.4. Note your answer for 8.24 does not have to be super detailed, just roughly describe the method you can use.

For 8.25a, it might be easiest to proceed in multiple steps. First, what observation can be made about y^3 and thus y? Try "substituting" this information into the question and proceeding from there.