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Show that every even positive integer …

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Show that every even positive integer is of the form 5q+1 or 5q+3 for some integer q

    • Posted by Mansi Sachdeva 5 years, 8 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years, 8 months ago

    Let p be any positive integer.

    On dividing p by 5 , Let M be Quotient and R be Remainder.


    Then , By Euclid division lemma , we have

    p = 5q+1 , where r = 0,1,2,3,4

    p = 5q , where R = 0

    p =5q + 1 , where R = 1

    p = 5q + 2 , where R = 2

    p = 5q + 3 , where R = 3

    p = 5q + 4 , where R = 4

    p = 5q , 5q+2 , 5q+4 are even values of N.

    Thus

    When p is odd , it is in the form of 5q , 5q+1 and 5q+3.

     

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