when a number is divided by 5 the remainder is 3 then what will be the remainder if the square of the number is divided by 5

Question

when a number is divided by 5 the remainder is 3 then what will be the remainder if the square of the number is divided by 5

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Savannah 2 weeks 2021-10-04T15:54:31+00:00 2 Answers 0 views 0

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    0
    2021-10-04T15:55:34+00:00

    example

    13 divided by 5 leaves 3 as remainder

    when u divide the square of 13 = 169 by 5

    it leaves 4 as remainder

    0
    2021-10-04T15:55:56+00:00

    Answer:

    Let x a number.

    Property of the modulus operator says that, for two integers a and b, on taking modulus with N.

    (a*b)%N = ( (a%N) * (b%N) )%N ……………………………………………….. (1)

    In given question, we have

    x%5 = 3 ………………………………………………………………………………………..(2)

    We need to find (x*x)%5

    By equation (1)

    (x*x)%5 = ( (x%5) * (x%5) )%5

    = (3 * 3)%5

    =9%5

    =4

    Answer : 4

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