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Thread: 2 New Problems

  1. Sep 12th, 2002, 05:13 PM #1
    SilverSprite
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    2 New Problems

    Something new? Hmmmmm.......ok

    How about an easy function problem.
    And then a harder sequence problem.

    1. If f(x)=9x+1 and g(x)=x^2. Find all values of x which satisfie f[g(x)]=g[f(x)]



    and ....



    2. If p and q belong to positive integers such that p/q=1+1/2-2/3+1/4+1/5-2/6+1/7+1/8 ... +1/478+1/479-2/480. Prove p is divisible by 641.
    YL says:"Few are those who see with their own eyes and feel with their own hearts."(Einstein)
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  2. Sep 12th, 2002, 07:06 PM #2
    SteveCRM
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    1. 0

    2....haven't looked at yet
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  3. Sep 13th, 2002, 07:18 PM #3
    SilverSprite
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    Hey the answer is 0 or -1/4 for the first one. But what about the second?
    YL says:"Few are those who see with their own eyes and feel with their own hearts."(Einstein)
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  4. Sep 14th, 2002, 09:34 AM #4
    SilverSprite
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    Guys somebody get the second one? Alright bugz you can post your solution since nobody can do it!
    YL says:"Few are those who see with their own eyes and feel with their own hearts."(Einstein)
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  6. Sep 14th, 2002, 11:12 AM #5
    bugzpodder
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    no thanx
    Massey RuleZ! ^-^__Cheers!__^-^ Massey RuleZ!


    Did you know that...
    The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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  7. Sep 14th, 2002, 11:55 AM #6
    SilverSprite
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    aiights
    YL says:"Few are those who see with their own eyes and feel with their own hearts."(Einstein)
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  8. Sep 14th, 2002, 12:34 PM #7
    mmiill
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    !

    p/q= 1/1+1/2+1/3+......+1/480 - 3*1/3(1/1+1/2+....+1/160)

    =1/161+1/162+....+1/480

    =641/(161*480)+.....641/(...*....)

    =641* N/Q

    641 is the prime number so q<> 641 *k => p=641*N
    ...
    mm
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  9. Sep 14th, 2002, 02:01 PM #8
    SilverSprite
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    nice job mmiill
    Last edited by SilverSprite; Sep 14th, 2002 at 02:14 PM.
    YL says:"Few are those who see with their own eyes and feel with their own hearts."(Einstein)
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