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List five integers that are congruent to 4 modulo 13:?

3 Answers

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  • 1 month ago

    You are looking for numbers that are 4 more than a multiple of 13.

    In other words, integers of the form:

    13k + 4

    Here k can be any integer {..., -3, -2, -1, 0, 1, 2, 3, ...}

    So for example, if k=0:

    13(0) + 4 --> 4

    If you divide 4 by 13, the remainder is clearly 4.

    If k = 1:

    13(1) + 4 --> 17

    If you divide 17 by 13, the remainder is again 4.

    At that point, you can see that you can just add (or subtract 13) and still get the same remainder.

    Answer:

    4, 17, 30, 43, 56, ...

  • 1 month ago

    4 mod13 = 17mod13 =30mod13 = 43mod13

    (0 mod n = kn for integer k, so all multiples of n are 0 mod n)

  • ?
    Lv 7
    1 month ago

    does 1 work?

    2?

    3?

    etc

    Do a few (many) more.

    List your results here as an update to your post. Then if need be we will take it from there. But you should see the pattern and be able to answer yourself with that list!

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