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Thread: Finding all natural numbers under a condition

  1. #1
    Nov 2010

    Finding all natural numbers under a condition

    hi, given N, how can one find all such N digit natural numbers such that the N least significant digits of any integral power of that number is the number itself?
    E.g if N =2
    then the required numbers are 25 and 76.
    because 25^2 = 625 and the 2 least significant digits of 625 are 25 which is the number itself , similary for any integral power of 25 and 76.
    Here N can be as large as 500 digits.
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  2. #2
    MHF Contributor
    Opalg's Avatar
    Aug 2007
    Leeds, UK
    See A018247 - OEIS and A018248 - OEIS for the numbers given by values of N up to about 100. I don't think there is any simple formula for the general case.
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