Question

1 Million Dollar Reward for Math answer:

Fermat's Last Theorem - the idea that A^x + B^y = C^z. There could only be solutions to the equation when A, B, and C have a common numerical factor.

Answer 1

Not kidding there is a billionaire looking for the answer to this and he has offered 1 million dollars.

Answer 2

IK! I saw this on ABC

Answer 3

A^x + B^y = C^z

Answer 4

Idk understand but I'll say 1 and 2

Answer 5

I mean solve for A by simplifying both sides of the equation, then isolating the variable.

Answer 6

Take the logarithm of both sides of the equation to remove the variable from the exponent.
x=ln(−By+Cz)ln(A)

Answer 7

to solve for x

Answer 8

Take the logarithm of both sides of the equation to remove the variable from the exponent.
y=ln(−Ax+Cz)ln(B)

Answer 9

@mathmale

Answer 10

to solve for y

Answer 11

To solve for X Take the logarithm of both sides of the equation to remove the variable from the exponent.
z=ln(Ax+By)ln(C)

Answer 12

Oops I meant Z

Answer 13

Solve for B by simplifying both sides of the equation, then isolating the variable.
By=−Ax+Cz

Answer 14

Solve for C by simplifying both sides of the equation, then isolating the variable.
Cz=Ax+By

Answer 15

If I am correct it cannot be solved.

Answer 16

given how exponentiation works even on the lower numbers you can quickly tell it won't work from powers of 2 and greater.

Answer 17

you can look at the powers of 2 to see this much.

3^2 = 9 which is 3*3 which is 3+3+3
4^2 = 16 which is 4*4 which is 4+4+4+4

see the problem if A B and C were all raised equally then the equation would work, but they aren't raised equally and the greater number you use for A B or C the greater the difference. it might work if you alter the powers

Answer 18

A^N + B^M = Z^O or perhaps A^N + B^N = Z^M where A = B

Answer 19

Fermat's last theorem has long been proven. The statement younsought to prove isn't even the statement in Fermat's last theorem.

Answer 20

*you sought

Answer 21

fermat's last theorem: an + bn = cn

Answer 22

or A^n+B^n=C^n

Answer 23

But he wrote Ax+By=Cz. Am I suppose to interpret that as A^x+B^y=C^z?

Answer 24

350-year-old mystery of Fermat's Last Theorem - the idea that A^x + B^y = C^z

Answer 25

When I wrote it I forgot to put the ^ symbols

Answer 26

And yes it does make a difference.

Answer 27

The statement should be:
For integer n>2, a^n+b^n=c^n admits no solution.

Answer 28

This is the problem that the billionaire posted.

Answer 29

Proven by Andrew Wiles in 1995.

Answer 30

I am not messing with you.
https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem

Answer 31

@thomas5267 then why is he offering a reward?

Answer 32

The margin note became known as Fermat’s Last Theorem,[17] as it was the last of Fermat’s asserted theorems to remain unproven

Answer 33

Probably the article claiming a billionaire offering a million dollar is a parody of some sort?

Answer 34

this is from that document or page you shared.

Answer 35

Second paragraph.

"The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. "

Answer 36

However without this part proven, there was no actual proof of Fermat's Last Theorem. Wiles spent almost a year trying to repair his proof, initially by himself and then in collaboration with Richard Taylor, without success.[119]

On 19 September 1994, on the verge of giving up, Wiles had a flash of insight that the proof could be saved by returning to his original Horizontal Iwasawa theory approach, which he had abandoned in favour of the Kolyvagin–Flach approach, this time strengthening it with expertise gained in Kolyvagin–Flach's approach.[120] On 24 October 1994, Wiles submitted two manuscripts, "Modular elliptic curves and Fermat's Last Theorem"[121] and "Ring theoretic properties of certain Hecke algebras",[122] the second of which was co-authored with Taylor and proved that certain conditions were met that were needed to justify the corrected step in the main paper. The two papers were vetted and published as the entirety of the May 1995 issue of the Annals of Mathematics. These papers established the modularity theorem for semistable elliptic curves, the last step in proving Fermat's Last Theorem, 358 years after it was conjectured.

Answer 37

http://abcnews.go.com/blogs/headlines/2013/06/billionaire-offers-1-million-to-solve-math-problem/

Answer 38

How?

Answer 39

Jk I wish I knew.

Answer 40

lol

Answer 41

It's really complicated, you need to have read "Annals of Mathematics" to come even close

Answer 42

Fermat's last theorem is proven. What the billionare wants is the Beal conjecture. The article is so poorly written no wonder you are confused.

Answer 43

Ok I see it now. I misunderstood it then because ABC wrote it lol anyways if they are trying to solve the beal conjecture let me find that.

Answer 44

Oh yes I thought that they were saying in the article that he was wrong when he supposedly proved it.

Answer 45

But yes as you have said it was solved by Andrew Wiley in 1994

Answer 46

Fermat's Last Theorem is this

\[\Large x^n + y^n = z^n\]

has no non-trivial integer solutions when n > 2

source:
http://www-history.mcs.st-and.ac.uk/HistTopics/Fermat's_last_theorem.html

Answer 47

I don't know where that page is getting Ax + By = Cz

Answer 48

oh, maybe they mean to say A^x + B^y = C^z

Answer 49

It is actually A^x + B^y = C^z

Answer 50

Beal's Conjecture
A generalization of Fermat's last theorem which states that if a^x+b^y=c^z, where a, b, c, x, y, and z are any positive integers with x,y,z>2, then a, b, and c have a common factor. The conjecture was announced in Mauldin (1997), and a cash prize of $1000000 has been offered for its proof or a counterexample

Answer 51

these two pages state that the theorem has been finally proved

http://mathworld.wolfram.com/FermatsLastTheorem.html
http://mathforum.org/dr.math/faq/faq.fermat.html

so I think there's something off here

Answer 52

Yes we have determined that it is Beal's conjecture

Answer 53

I wouldn't be surprised if someone is working on Beal conjecture now. After all Andrew Wiles worked alone for 6 years before coming up with a proof.

Just to clarify, Fermat's last theorem was proven by Andrew Wiles in 1995. The billionaire Andy Beal want the proof of a different conjecture named Beal conjecture and will give a million dollar to the person who proved it. Beal conjecture is a generalisation of Fermat's last theorem.

Answer 54

1994 but yes.

Answer 55

Also @thomas5267 I wouldn't recommend using Wikipedia as a source.

Answer 56

ah I see now, nvm what I posted

Answer 57

But since there are so many other sources then it could very well be plausible.

Answer 58

Wikipedia is more than alright when you are engaging in an informal discussion. When you are writing any formal essay, Wikipedia is a big no-no.

Answer 59

Yes I was just simply pointing out that Wikipedia is not necessarily a very good source. Yes for these purposes it is alright.

Answer 60

I won't use Wikipedia if my grades depends on it. I do use Wikipedia as a starting point and for the references in Wikipedia.

Answer 61

So since everyone on OpenStudy is looking at this any ideas?

Answer 62

lol jk

Answer 63

Sorry but I truly need to leave now I will talk to and maybe help many of you later after I am done with tutoring tonight.

Answer 64

this person/page invested a lot of time into trying to find counterexamples

http://norvig.com/beal.html

but didn't find any. So it means that if there are counterexamples, then they are so large that they won't be found any time soon. If there are no counterexamples, then the actual proof itself is going to be nearly impossible unless you're a very gifted mathematician

Answer 65

so there's a reason why there's a lot of money put up for this problem