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Math Help - Number theory equations

  1. #1
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    Number theory equations

    Solve the following equations positive integers:

    (i) a!+b!+c!=d!

    (ii) a!+b!=25*c!

    (iii)a!=b^2

    For the first two one , i have no idea how to begin . But the third one I may use Bertrand's Postulate some where. Could anyone give me some ideas??
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Number theory equations

    Quote Originally Posted by Sonifa View Post
    (i) a!+b!+c!=d!
    Hi Sonifa!

    Let's pick a \le b \le c.

    Then we have d! = a!+b!+c! \le 3c!.
    Therefore d \le 3.
    Now enumerate all possibilities taking this bound into account...
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