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Mathematics prize ups the ante to $1 million

Andrew Beal

Andrew Beal, a banker and mathematics enthusiast, offered US$1 million to anyone who can find a proof for the number-theory conjecture that bears his name.

Posted on behalf of Devin Powell.

A billionaire businessman from Dallas, Texas, has sweetened the pot for a number-theory prize that has remained unclaimed for 16 years. After putting up US$5,000 in 1997 for a solution to the Beal conjecture and then upping it to $100,000 in 2000, Andrew Beal has now raised the stakes yet again to $1 million, the American Mathematical Society (AMS) announced today.

That puts the Beal Prize on equal footing with the Clay Mathematics Institute’s million-dollar Millennium Prizes, announced in 2000, which address seven extraordinarily difficult problems in mathematics. Only one of those problems has been solved to date, but the man who solved declined to accept the prize.

The Beal Conjecture is related to Fermat’s Last Theorem, which famously states that Ax + Bx = Cx has no solution if A, B and C are positive integers and x is an integer greater than 2. A lawyer named Pierre de Fermat had claimed during the seventeenth century to have a proof for this statement, but if he did, it was lost to history. It wasn’t until 1995 that mathematicians Andrew Wiles and Richard Taylor formally published the proof known today.

Beal, apparently unwilling to wait 350-plus years, started with a similar equation, Ax + By = Cz. If A, B, C, x, y and z are positive integers greater than 2, he posited, then A, B, and C must share a common factor — meaning that they must be divisible by the same number.

The statement of his conjecture is a stronger form of Wiles and Taylor’s result: the truth of the Beal Conjecture also implies that of Fermat’s Last Theorem, but not vice versa.

To claim the money, a solution must be published in a “respected” peer-reviewed journal and reviewed by an AMS committee. No one has yet done so. Some have instead tried to claim the prize by searching for counter-examples, using simpler math and aided by computer programs.

Comments

  1. Alexandra Pacheco said:

    Common Factor: 4

    A(x) is 8(2)
    B(x) is 12(2)
    Cx is 16(2)

    So then
    8(2) + 12(2) = 16(2) then
    64+144=208 then

    (64/4)+(144/4)=208/4

    16+36=52

    its a positive integer even number and divisible by all numbers and greater than 2

    1. Alejandra Diaria said:

      That’s correct, however the Fermat’s Theorem states that x must be greater than 2, not equal or greater than 2… So x must start from 3…

  2. rohit j said:

    If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor.
    Ax+By = Cz
    Ax = 24
    By = 25
    Ax+By = 49
    Ax+By = 49 + A value = 1 + B value = 2 = 52 (49+1+2 =52)
    A+B=2
    52/2=26
    Cz =26
    cz*3=78
    x+y+z =78
    A+B+C=3
    78/3=26
    so, the common factor is 3*26

  3. Shivavinoban Sivakrishnanathan said:

    hallo sir,
    i got the correct answer. how to contact you?

    Report this comment Cancel report
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  4. Bruno Osvaldo Rodríguez Cagna said:

    Las matemáticas son sencillas, lo que las hace difíciles es olvidar sus bases y principios.
    La potenciación es consecuencia de la multiplicación y la multiplicacion de la aditividad. De esto llego a la respuesta y demostración:
    para que Ax+By=Cz (A,B,C enteros positivos, y X,Y,Z enteros positivos mayores que 2, y A,B,C con un factor comun) necesariamente Cz=2Ax=2By si el factor comun es igual a 2. Si el fator comun fuera 3 entonces la funcion tendria que ser Ax+By+Dt=Cz (x,y,t,z son numeros que potencian A,B,C,D)

    como llego a la conclusión? Ax debe de ser igual a By
    ejemplo A=2 y x=9
    B=8 y y=3
    Ax= 2*2*2*2*2*2*2*2*2
    By= 8*8*8=(2*2*2)*(2*2*2)*(2*2*2)

    Ax+By=2*2*2*2*2*2*2*2*2+(2*2*2)*(2*2*2)*(2*2*2)=2Ax=2By=Cz
    2*512=1024
    Cz= 4 a la 5º= 1024

    otro ejemplo
    A=2 x=15 entonces Ax=32765
    B=8 y=5 entonces By=32765
    C=4 z=8

    entonces Ax=32768 y By=32768
    2Ax=32768*2= 65536
    Cz=65536

    lo interesante es la relacion entre los exponentes:
    en el primer ejemplo x=9 y Z=5
    si x/2=4.5
    4 a la 4.5=512
    entonces 4 a la 4.5=Cz/2

    en el segundo caso
    x=15
    x/2=7.5
    entonces 4 a la 7.5= Cz/2

    esto se da porque C=4=2*2 entonces (2*2) a la 4.5=512 o (2*2) a la 7.5=32768

    Otro ejemplo
    si A=2 x=15
    si B=8 y=5
    C=16 z=4

    Ax=32765
    Bz=32765
    Cz=32765+32765=65536

    Creo que esto demuestra que Cz=2Ax=2By

    Google traductor

    The math is simple, which makes them difficult is forgetting its bases and principles.
    The enhancement is due to the multiplication multiplication and additivity. From this came the response and demonstration:
    that Ax By Cz = (A, B, C positive integers, and X, Y, Z positive integers greater than 2, and A, B, C with a common factor) Cz = 2Ax necessarily = 2By if the common factor equals to 2. If the common fator was 3 then the function would have to be Dt = Ax By Cz (x, y, t, z are numbers that enhance A, B, C, D)

    as I conclude? Ax must be equal to By
    example A = 2 and x = 9
                 B = 8 and y = 3
    X = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
    By = 8 * 8 * 8 = (2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2)

    By Ax = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 (2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2) = 2Ax = 2By = Cz
    2 * 512 = 1024
    Cz = 4 to 5 ° = 1024

    another example
    A = 2 x = 15 then Ax = 32765
    B = 8 y = 5 then By = 32765
    C = 4 z = 8

    then Ax = By = 32768 and 32768
    2Ax = 32768 * 2 = 65536
    Cz = 65536

    what is interesting is the relationship between the exponents:
    in the first example x = 9, and Z = 5
    if x / 2 = 4.5
      4 to the 4.5 = 512
    then 4 to the 4.5 = Cz / 2

    in the second case
    x = 15
    x / 2 = 7.5
      then 4 to the 7.5 = Cz / 2

    this is because C = 4 = 2 * 2 then (2 * 2) to the 4.5 = 512 or (2 * 2) to 7.5 = 32768
     
    another example
    if A = 2 x = 15
    if B = 8 y = 5
    C = 16 z = 4

    Ax = 32765
    Bz = 32765
    Cz = 32765 32765 = 65536

    I think this shows that Cz = 2Ax = 2By

    1. Bruno Osvaldo Rodríguez Cagna said:

      Saludos desde Argentina-Tucuman 😉

  5. William S. Walker said:

    W Bill S Walker
    Shared publicly – 4:33 AM
    #PuntWW

    Ax+By=Cz Solved 02.24.2014
    #PingMe plus.google.com/+WBillSWalker #Curve Formulas
    Solve A Right Triangle Ax+By+Cz=180 Degrees
    Angle A = 45 Degrees ( x = 1 squared ) = .07710678117
    +
    Angle B = 45 Degrees ( y = 1 squared ) = .07710678117
    Equals
    Angle C = 90 Degress ( z = square root of 2 ) = 1.41421356234
    1.41421356234 divided by 90 degrees is
    equal to .015713484026
    .015713484026 times 45 degrees = .0771067811
    .015713484026 times 90 degrees = 1.41421356234 length of side z

    Solve and Oblique Triangles Ax+By+Cz=360 Degrees
    Angle A = 90 Degrees ( x = 2 squared ) = .1.41421356234
    +
    Angle B = 90 Degrees ( y = 2 squared ) = 1.41421356234
    Equals
    Angle C = 180 Degress ( z = square root of 8 ) = 2.828427124746
    2.828427124746 divided by 180 degrees is
    equal to .015713484026
    .015713484026 times 90 degrees = .1.41421356234
    .015713484026 times 180 Degrees = 2.828427124746 length of side z
    #PuntWW
    A+B=C Square root of 8 = 180 degrees = 2.828427124746 = divided by 2 = 1.41421356234 or 90 Degrees
    PI = 0
    PC=90
    PT=90

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