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Number Theory help

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Number Theory help
by Kevin Song - Saturday, March 27, 2021, 7:32 PM

Hello, I don't know how to do 5.27. I don't know how to prove it; I tried using mod 4 but that didn't work. 

Picture of John Lensmire
Re: Number Theory help
by John Lensmire - Monday, March 29, 2021, 10:14 AM

For clarity, let's summarize why mod 4 doesn't work. We know any square is 0 or 1 (mod 4). Thus the sum of 3 squares is either 0, 1, 2, or 3 (mod 4). But since this is all possibilities it is not very helpful.

For purposes of this problem, we could say 4 is not "large enough" as a mod. Thinking about your answers from 5.26 (where you listed possible squares mod m for m < 10) see if you could find another mod that might work.

Hope this helps a bit!