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Math Help - Prime Divisors Positive Difference

  1. #1
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    Prime Divisors Positive Difference

    For a composite positive integer x, denote by pd(x)the smallest positive difference between any two prime divisors of x. Find the smallest possible value of pd(x) for composite x of the form x=n^100+n^99+...+n+1, where n is a positive integer.
    It is a very typical question. after solving for a long time, i come at the same point...
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  2. #2
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    Re: Prime Divisors Positive Difference

    I m not sure about its proof but sending example according to this statement.

    Example : Factors of 273 = 13 * 7 * 3

    In these factors 13 and 7 are prime numbers

    So pd(273) = 13 - 7 = 6

    This would help you better Finding Factors of Numbers
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