Mathematics

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Show that 27 x 23^n + 17 x 10^2n is divisible by 11 for all positive integers n. I know that modulos should aid in answering this problem,

  • Mathematics -

    27= 2 mode 5
    23= 2 mode 1
    17= 1 mode 6
    10^2n= 100^n
    100= 1 mode 9
    So the problem reduces to
    5*1^n+6*1^n
    =5+6
    =11

  • Mathematics -

    oops,typo error.

    100=9 mode 1 the rest is correct.

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