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Math Help - [SOLVED] congruent modulo n

  1. #1
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    Thumbs up [SOLVED] congruent modulo n

    For the statement "a is congruent to b modulo n"
    Which of the following definition is correct.

    a) a - b is divisible by n.

    b) a - b is a multiple of n.

    or whether both are acceptable.


    Whether "a is congruent to a mod 0" is true?

    a - a = 0 is divisible by 0 is wrong. But 0 is a multiple of 0 is correct. So whether to consider
    the definition (a) or definition (b).
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  2. #2
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    for every  a \in \mathbb{R}, a = a + k(0),  k \in \mathbb{N}
    so a \equiv a ~mod ~0.

    for this case, just use definition (b)

    regards
    Last edited by Plato; December 8th 2009 at 07:49 AM. Reason: LaTeX
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  3. #3
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    Quote Originally Posted by sudeepmansh View Post
    For the statement "a is congruent to b modulo n"
    Which of the following definition is correct.

    a) a - b is divisible by n.

    b) a - b is a multiple of n
    The correct answer: in mathematics, it is not customary to argue about definitions.

    That said, both MathWorld and Planet Math use (a), and Planet Math specifies that n\ne 0. If I am not mistaken, both definitions are equivalent if n\ne 0.

    I agree with the OP's assessment of "a is congruent to a mod 0".
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