Sum of two squares

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  • #1
ehrenfest
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Homework Statement


Prove that no prime three more than a multiple of four is a sum of two squares. (Hint: Work modulo 4.)


Homework Equations





The Attempt at a Solution



a^2+b^2=4n+3=3 mod 4 is impossible if you look at the possibilities of a^2 and b^2.

I did not use the fact that the number is prime. Am I missing something?
 

Answers and Replies

  • #2
Dick
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Doesn't seem likely, does it?
 
  • #3
ehrenfest
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Doesn't seem likely, does it?

What doesn't seem likely?
 
  • #4
Dick
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"Am I missing something?" doesn't seem likely. You checked squares are 0 or 1 mod 4. So the sum of two of them doesn't equal 3. Looks pretty bulletproof to me.
 
  • #5
Defennder
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Homework Statement


Prove that no prime three more than a multiple of four is a sum of two squares. (Hint: Work modulo 4.)
What does "prime three" here mean?
 
  • #6
HallsofIvy
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What does "prime three" here mean?

It doesn't mean anything- but I did a double take myself when I read that. Perhaps commas would help: No prime, three more than a multiple of four, is a sum of two squares
 
  • #7
ehrenfest
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It doesn't mean anything- but I did a double take myself when I read that. Perhaps commas would help: No prime, three more than a multiple of four, is a sum of two squares

In my defense, Loren Larson (who is all-knowing) didn't think this sentence required any commas.
 
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