Recent content by Inviction

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    Modular Arithmetic: 8^7 ≡ (-5)^7 (mod 13) and (25)^3 ≡ (-1)^3 (mod 13)?

    Oh wow thanks, that was totally not intuitive for me for some reason, but I see it much more clearly now. I just started doing modular arithmetic and never realized the same rules still apply. I guess "≡ (mod n)" is the same as "=" as far as any calculations are concerned?
  2. I

    Modular Arithmetic: 8^7 ≡ (-5)^7 (mod 13) and (25)^3 ≡ (-1)^3 (mod 13)?

    I have a simple question: Why does 8^7 ≡ (-5)^7 (mod 13) and (25)^3 ≡ (-1)^3 (mod 13)? In essence I want to show that 8^7 + 5^7 = 13^7, so that both sides of the equation ≡ 0 (mod 13) and therefore 8^7 ≡ (-5)^7 (mod 13). I know that in a field of characteristic p>0, (x + y)^p = x^p +...