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By using Euclid Division Lemma, Show that one and only one out of n, n+ 1,n+ 2 and n+ 3 is divisible by 4.​

By Emma

By using Euclid Division Lemma, Show that one and only one out of n, n+ 1,n+ 2 and n+ 3 is divisible by 4.​

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Emma

The daily expenditure of a man is Rs. 3.30p. What must be his annual income so that his yearly savings may be Rs. 350.75p.?​

3.
In the following cases, find out if the first number is a factor of the 2nd
number (use the rules, don’t do the actua

1 thought on “By using Euclid Division Lemma, Show that one and only one out of n, n+ 1,n+ 2 and n+ 3 is divisible by 4.​”

  1. Step-by-step explanation:

    Solution:

    let n be any positive integer and b=3 where is the quotient and r is the

    n =3q+r

    remainder

    0_ <r<3

    so the remainders may be 0,1 and 2 so n may be in the form of =1,3q+2

    CASE-1

    IF N=3q

    n+4=3q+4

    n+2=3q+2

    here n is only divisible by 3

    CASE 2

    if n = 3q+1

    n+4=3q+5

    n+2=3q=3

    here only n+2 is divisible by 3

    CASE 3

    IF n=3q+2

    n+2=3q+4

    n+4=3q+2+4

    =3q+6

    here only n+4 is divisible by 3

    l 56

    HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE

    Reply

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