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    what are all the steps to solve this equation?

    97645643 – 6X * lower part( 97645643 / 6X)=X

    thank you
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    Just to clarify to everyone, this is the expression:

    97645643-6x \left\lfloor \dfrac{97645643}{6x}\right \rfloor = x
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    If x is assumed to be an integer, you can move the 6x inside of the floor operation. This then cancels the 6x in the denominator. You are left with 97645643 - 97645643 = x
    so x = 0

    I'm not sure if this is a legitimate solution as this implies that 0 is in the denominator.
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    (Original post by morgan8002)
    If x is assumed to be an integer, you can move the 6x inside of the floor operation. This then cancels the 6x in the denominator. You are left with 97645643 - 97645643 = x
    so x = 0

    I'm not sure if this is a legitimate solution as this implies that 0 is in the denominator.
    This won't yield integer solutions for x.
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    thank you
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    97645643-6x \left\lfloor \dfrac{97645643}{6x}\right \rfloor = x

    Rearranging..

    \dfrac{97645643}{x}\right \rfloor =1+6 \left\lfloor \dfrac{97645643}{6x}\right \rfloor

    So x is a factor of 97645643.
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    but what are all the values of x, and how to calculate
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    (Original post by gerva)
    but what are all the values of x, and how to calculate
    As argued above, x is an integer which is 5 mod 6, which divides that long number. Sadly it's hard to factor that number.

    Notice that b \lfloor \dfrac{a}{b} \rfloor is "a rounded down to the nearest multiple of b". Hence a - b \lfloor \dfrac{a}{b} \rfloor is "the difference between a and the nearest multiple of b less than a": that is, it is a \pmod b.

    That is, we seek x such that 97645643 \equiv x \pmod{6x}.

    Does that help? (You may find the Chinese Remainder Theorem useful in seeing from another angle where this came from.)
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    yes, thank you
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    (Original post by gerva)
    yes, thank you
    Does it? I can't really see that it does, but if it helped… :P Mind writing out your solution, because I still haven't solved it except by computer?
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    (Original post by Smaug123)
    Does it? I can't really see that it does, but if it helped… :P Mind writing out your solution, because I still haven't solved it except by computer?
    This one, by luck, comes out very quickly using Fermat's factorisation method.
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    is a help in more
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    if you want to see what I'm doing http://albericolepore.altervista.org/
 
 
 
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