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Math Help - Divisibility

  1. #1
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    Divisibility

    Since it is commonly known that if an integer x is not divisible by 3, then x = 3q + 1 or x = 3q + 2, does it mean that if an integer y is not divisible by 11, then y = 11q + 1 or y = 11q+2 or y=11q + 3 or …or y = 11q+10 for some integer q?
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  2. #2
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    Quote Originally Posted by novice View Post
    Since it is commonly known that if an integer x is not divisible by 3, then x = 3q + 1 or x = 3q + 2, does it mean that if an integer y is not divisible by 11, then y = 11q + 1 or y = 11q+2 or y=11q + 3 or …or y = 11q+10 for some integer q?
    Yes. You may read about the division algorithm to understand why this must be the case.
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