Show that if $n\equiv 3(mod 4)$ then n is not the sum of the square of 2 intergers
Please, help

Question

Show that if $n\equiv 3(mod 4)$ then n is not the sum of the square of 2 intergers
Please, help

superdavesuper · Answer

just posting 4 fun eh? ;) http://math.stackexchange.com/questions/496255/can-an-integer-of-the-form-4n3-written-as-a-sum-of-two-squares

loser66 · Answer

Not for fun at all. :) There are a bunch of proof on internet but I didn't see the elegant one yet. :)

superdavesuper · Answer

how about top of P.2 here http://math.uga.edu/~pete/4400twosquares.pdf it looks pretty good to me

loser66 · Answer

Oh, yes!! thank you so much. The solution is elegant since it is so simple. To me, if we can "cook" a good meal with less material, then the job is a beautiful art.

loser66 · Answer

The solution on stackexchange is good enough to me.

superdavesuper · Answer

anything on stackexchange is good enough to me since i dont dare posting on there lol

imho the second proof i linked is actually simpler thou ;)