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Math Help - [SOLVED] Congruent Modulo

  1. #1
    rexsi
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    [SOLVED] Congruent Modulo

    I have an assignment due tommorow and I am completely lost I was wondering if anyone could give me a hand hehe.

    The two silly questions I am stuck on are:

    Find all numbers between 10 and 20 which are congruent to 173 modulo 3

    and.....


    Find all numbers between 10 and 20 which are congruent to -173 modulo 4

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  2. #2
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    Quote Originally Posted by rexsi
    I have an assignment due tommorow and I am completely lost I was wondering if anyone could give me a hand hehe.

    The two silly questions I am stuck on are:

    Find all numbers between 10 and 20 which are congruent to 173 modulo 3

    and.....


    Find all numbers between 10 and 20 which are congruent to -173 modulo 4

    You need,
    x\equiv 173 \mod 3
    But,
    173\equiv 2\mod 3
    Thus, (transitive property of congruences)
    x\equiv 2\mod 3
    But, 10\leq x\leq 20.
    Thus, x=11,14,17,20
    -----------
    You need,
    x\equiv -173 \mod 4
    But,
    -173\equiv 3\mod 4
    Thus, (transitive property of congruences)
    x\equiv 3\mod 4
    But, 10\leq x\leq 20
    Thus, x=11,15,19

    \mathbb{Q}.\mathbb{E}.\mathbb{D}
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