[代數] 平方和

[jacky7987 (憶)]

Prove that for all element z in a finite field E is a sum of two squares
(If z=a^2 is a square, then we may write z=a^2+0^2)

Hint: Let G be a finite group, and let S and T be two nonempty set.
      Then, either G=ST or |G|≧|S|+|T|

毫無頭緒QQ
感謝大家的幫忙

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推 XII         :{a^2:a in E}與{z-b^2:b in E}交集非空
→ jacky7987   :不好意思還是不甚了解:(
推 k75715      :想一下交集非空會發生什麼事 假設一下裏面的元素
→ jacky7987   :某些z-b^2=a^2但是似乎不能推得全部的?
→ jacky7987   :所以我必須要證明右邊那個集合包含在左邊裡面?
推 yusd24      :邏輯問題..對於任意的 z ，證明交集非空即可
→ jacky7987   :喔:D
→ jacky7987   :感謝大大:)