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Math Help - what is the second last number

  1. #1
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    what is the second last number

    So i have 7^900413 and want to know what the second last number is if we had done the calculation.
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  2. #2
    Super Member
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    Quote Originally Posted by Berntsson View Post
    So i have 7^900413 and want to know what the second last number is if we had done the calculation.
    Start this way:

    7^0 = 001
    7^1 = 007
    7^2 = 049
    7^3 = x43
    7^4 = x01
    7^5 = x07
    7^6 = x49
    7^7 = x43
    7^8 = x01
    7^9 = x07
    Next to the last digit is either 0 or 4.
    Notice that the digits occur in pairs.
    The zero first occurs when the exponent is:
    0,4,8,12,16,20,etc...
    or in steps of 4.

    900413 divided by 4 is some number with remainder of 1
    Thus the last two digits of 7^900412 = 01

    You need to do one more calculation.

    .
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