*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 *A ^{x}* +

*B*=

^{x}*C*

^{x}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, *A ^{x} *+

*B*=

^{y}*C*. If

^{z}*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.

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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

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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…

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16(2) <> 208

16(2)= 256.

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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

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hallo sir,

i got the correct answer. how to contact you?

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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

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Saludos desde Argentina-Tucuman 😉

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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