title: Binary modulo operation
body: <p>My apologies, this question is now redirected to</p>
  <p><a href="https://math.stackexchange.com/questions/2535220/binary-modulo-operation">this web page in math forum</a>.</p>
  <p><strike>Empirically, I can know that (a+b+c) mod 2 = (a-b-c) mod 2.</p>
  <blockquote>
  <p>e.g.,)</p>
  <p>1+2+3 = 6, 6 mod 2 = 0<br />
  1-2-3 = -4, -4 mod 2 = 0</p>
  <p>1+2+4 = 7, 7 mod 2 = 1<br />
  1-2-4 = -5, -5 mod 2 = 1</p>
  </blockquote>
  <p>It seems that it is only possible when we use binary modulo (mod 2).</p>
  <p>Is there any formal proof for this?
  </strike></p>