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Math Help - this is........ uhmmm... 5, isn't it?

  1. #1
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    Talking this is........ uhmmm... 5, isn't it?

    How many natural number n with n\leq2009 which satisfies lcm(n,2009)+gcd(n,2009)=n+2009 ?
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  2. #2
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    Quote Originally Posted by GTK X Hunter View Post

    this is........ uhmmm... 5, isn't it?

    How many natural number n with n\leq2009 which satisfies lcm(n,2009)+gcd(n,2009)=n+2009 ?


    May be, but won't you need to explain why?

    CB
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  3. #3
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    Quote Originally Posted by GTK X Hunter View Post
    How many natural number n with n\leq2009 which satisfies lcm(n,2009)+gcd(n,2009)=n+2009 ?
    Since more errors occur at the start or end points, my guess is that you missed that 1 works as well as 2009.
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  4. #4
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    no i didn't miss 1 nor 2009...
    the 5 natural numbers satisfying that equation are 1,7,41,287,2009 ryt???!
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  5. #5
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    Quote Originally Posted by GTK X Hunter View Post
    no i didn't miss 1 nor 2009...
    the 5 natural numbers satisfying that equation are 1,7,41,287,2009 ryt???!
    Well those do, but do you not have to prove that there are no others?

    CB
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  6. #6
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    Quote Originally Posted by CaptainBlack View Post
    Well those do, but do you not have to prove that there are no others?

    CB

    Hi CB

    I might be able to attempt on that

    Let gcd(n,2009) = x
    lcm(n,2009) = n2009/x
    Substitute and solve the quadratic, it comes in a nice form. And, this infact can be generalized.

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  7. #7
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    Quote Originally Posted by GTK X Hunter View Post
    no i didn't miss 1 nor 2009...
    the 5 natural numbers satisfying that equation are 1,7,41,287,2009 ryt???!
    did u miss 49?
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  8. #8
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    Talking

    Quote Originally Posted by aman_cc View Post
    did u miss 49?

    ooouuuppsss... sorry...
    yeap, i miss 49, good
    So there are 6 natural numbers including 49 satisfying the equation ryt??
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