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Math Help - Fermat, computers, and a smart boy

  1. #1
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    Fermat, computers, and a smart boy

    A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

    x=2233445566,
    y=7788990011,
    z=9988776655

    He announces these 3 numbers and calls for a press conference where he is going to present the value of N (to show that

    x^N + y^N = z^N

    and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug.

    How did the boy figure out that the scientist was wrong?
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  2. #2
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    Quote Originally Posted by yiyayiyayo
    A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

    x=2233445566,
    y=7788990011,
    z=9988776655

    He announces these 3 numbers and calls for a press conference where he is going to present the value of N (to show that

    x^N + y^N = z^N

    and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug.

    How did the boy figure out that the scientist was wrong?

    The Least Significant Digit (LSD) of x^N is 1, and the LSD of y^N is 6,
    so the LSD of x^N+y^N is 7 which is not the LSD of z^N which is 5.

    RonL
    Last edited by CaptainBlack; January 30th 2006 at 04:13 AM.
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  3. #3
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    Quote Originally Posted by yiyayiyayo
    A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

    x=2233445566,
    y=7788990011,
    z=9988776655

    He announces these 3 numbers and calls for a press conference where he is going to present the value of N (to show that

    x^N + y^N = z^N

    and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug.

    How did the boy figure out that the scientist was wrong?
    The 10-year old boy knows how to add.

    The last digit of x is 6.
    6^N will have 6 as the last digit.

    The y has 1 at the end, and 1^N will give 1 always.

    The z has has 5 at the end, and 5^N will give 5 at the end too.

    The young lad added 6+1 and he was getting 7, not 5.

    ----------------
    Yeah. Steroids, steroids for this finger.

    -----------------------
    Also, I just cannot get off the "mana" re all new news/articles about my Pittsburgh Steelers! It's been a long time coming. I will not miss them for any Math forum. I am not from the 'Burgh but I am a member of the Steelers Nation since 1974! Isn't nice to have Internet?! Instant news, pictures, voice broadcast, ....
    If ThePerfectHacker would delete this, I would sue him in court. Yeah.
    Last edited by ticbol; January 30th 2006 at 03:47 AM.
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  4. #4
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    The ten year old boy was Gauss, skip the last digit! he just added them up
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  5. #5
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    Cool

    Quote Originally Posted by ThePerfectHacker
    The ten year old boy was Gauss, skip the last digit! he just added them up
    I don't want to comment on anybody's answer, but since this answer is yours (get the hint?), I will break my policy on this.

    The question mentioned Fermat (you have a poll on greatest mathemations and you don't recognize Fermat's Last Theorem?) so the N here is greater than 2. So even if the lad added successfuly the given X,Y,Z, your answer is wrong because that would have been for N=1.

    ticbol

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    Been from short vacation, didn't go to work now so can answer here now in this time-window.
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  6. #6
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    Do you think Fermat had a proof as he claims? Or do you think he was found it for only a few cases and assumed it was always true?
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  7. #7
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    The Human Comedy

    I think it is pretty obvious that he lied. I also think it is very funny. And I also think that your joke earlier in this thread was funny.

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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by MathGuru
    I think it is pretty obvious that he lied. I also think it is very funny. And I also think that your joke earlier in this thread was funny.

    Lied is probably the wrong word. Any body who has ever done any real
    maths will have thought they have proven a result, but the proof has
    been fallacious (wrong).

    RonL
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  9. #9
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    Quote Originally Posted by ThePerfectHacker
    Do you think Fermat had a proof as he claims? Or do you think he was found it for only a few cases and assumed it was always true?
    That is not the idea, whether he proved it or not. Your answer to the question here is wrong. You should have seen that adding X and Y as given is wrong way because those are of n=1. That is the idea.

    ticbol.
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  10. #10
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    Quote Originally Posted by yiyayiyayo
    A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

    x=2233445566,
    y=7788990011,
    z=9988776655

    He announces these 3 numbers and calls for a press conference where he is going to present the value of N (to show that

    x^N + y^N = z^N

    and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug.

    How did the boy figure out that the scientist was wrong?
    Hello i have a simple way to do that:

    we have got x+y>z
    so x^n +y^n = ((x+y)^n)-K(see above) >z^n for a->a^n is a strictly growing up function!
    K is the positive integer for wich x^n+K+y^n =(x+y)^n (you know the formula to get K) don't you!
    (qued) this demonstration is stupid i should'nt have drink a little sup of paddy before lurking that site but they are indeed so much reason for numbers not to satisfy the "equation" that's its a shame nobody (except anybody) can give a simple solution to this "riddle"
    see you!
    Last edited by SkyWatcher; February 2nd 2006 at 07:26 AM.
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  11. #11
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    Quote Originally Posted by ticbol
    That is not the idea, whether he proved it or not. Your answer to the question here is wrong. You should have seen that adding X and Y as given is wrong way because those are of n=1. That is the idea.

    ticbol.
    It was a joke (I was not serious).
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