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The modulus of a number relative to a base is the positive remainder when itis divided by that base. So

-24 mod 7 = (-28 + 4) mod 7 = -28 mod 7 + 4 mod 7 = 4 mod 7 = 4while

24 mod 7 = (21 + 3) mod 7 = 21 mod 7 + 3 mod 7 = 3 mod 7 = 3.

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Q: Why does -24 mod 7 equal 4 but 24 mod 7 equal 3?
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