Number Theory Related Questions by Balaji

  • 8August
  • 2014
  • 2
    2k
    (55555.......2013 times ) divided by 440, what is the remainder ?

    a) 5



    b) 155



    c) 115



    d) 125


    answer choice c

    solution


    N/8 remainder =3
    N/5 remainder =0


    N=8k+3


    N can take -27,115,203,291,379


    N=440c + 115


     
    The product of two non-coprime number is 1080. how many such pairs are possibles ?



    a) 16



    b) 4



    c) 12



    d) 15



    answer choice c

    solution


    a*b=1080
    no of factors =4*4*2=32

    no of ways of writing 1080 as a product of two non coprime no = 16-4=12
     
    (234)n


    (1ab)n/(b21)n


    find (a+b)

    a) 11



    b) 8



    c) 7 or 11



    d) 9



    answer choice d



    solution



    4+b=n+1

    where b=4

    8=n+1

    n=7

    4+a=n+2

    4+a=9

    a=5

    a+b=9