mod equations problem...

Hi!
I need to prove that there is *no* solution to the equation:
x^2 + y^2 = 3(mod4)

I tried to assume there is a solution, meaning, there are X,Y in Z so that:
x^2 + y^2 = 3 + 4*k.

I tried to reach a contradiction, but alas, I did not succeed :-\

Help?
Thank you very much, in advance!

Hello,

Quote:

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Originally Posted by aurora

Hi!
I need to prove that there is *no* solution to the equation:
x^2 + y^2 = 3(mod4)

I tried to assume there is a solution, meaning, there are X,Y in Z so that:
x^2 + y^2 = 3 + 4*k.

I tried to reach a contradiction, but alas, I did not succeed :-\

Help?
Thank you very much, in advance!

---

Find all the possibilities.

Attachment 6682

The numbers are the modulus with respect to 4 :)
Does it help ?

Quote:

---

Originally Posted by aurora

Hi!
I need to prove that there is *no* solution to the equation:
x^2 + y^2 = 3(mod4)

I tried to assume there is a solution, meaning, there are X,Y in Z so that:
x^2 + y^2 = 3 + 4*k.

I tried to reach a contradiction, but alas, I did not succeed :-\

Help?
Thank you very much, in advance!

---

If is even then .
If is odd then .
Thus, .
Thus, it is impossible.

Thank you very much, both of you!