Solve this and win USD $1,000,000
A^3 + B^3 = C^3 where positive integers A, B and C do not have a common prime factor.
There are even additional ways to win this Million Dollar prize:
You are not limited to only cubes. You can change the powers so that Ax + By = Cz where x, y and z are all positive integers greater than 2.
This is called the Beal Conjecture which is still unproven:
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.
To win the $1 million dollar prize you can either prove it or disprove it by solving it, that is, give a counter example.
A counter example is just solving the equation with integers that do not have a common prime factor that would prove the Beal Conjecture to be false.
We can try A = 3 and B = 4 and x = y = z = 3 then 33 = 27 and 43 = 64 so that 27 + 64 = 91
But the cube root of 91 = 4.49794... is not an integer so that doesn't win.
Let's try A = 3 and B = 6 then 33 + 63 = 27 + 216 = 243 = 35 = 33 + 63
Wow! I just won a million dollars ... almost.
The disqualifier is A, B and C have a common prime factor of 3
How about 13 + 23 = 32
Although this is true, one of the exponents is 2 and therefore disqualified.
The Beal Conjecture was formulated by mathematician and banker, Andrew Beal in 1993. He started offering a reward for proving or disproving it twenty years ago. He has increased the reward a few times and it now stands at $1 Million Dollars USD.
The prize money is being held by the American Mathematical Society (AMS)
More info here:
http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize
And here:
https://en.wikipedia.org/wiki/Beal_conjecture
Some more examples of almost winners:
http://www.ams.org/notices/199711/beal.pdf
The official rules and how to submit your winning solution:
http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize-rules
If a steemian wins this prize, he or she can instantly become a whale, so be sure to resteem!
🐟 ..................... 🐳
Have fun with this.
Good Luck to all.
This is wrong...or at least I hope it is since Fermat's last theorem states that A^n+B^n = C^n is never true for any A,B,C, and n > 2....
In Beal's Conjecture the exponents can have different values so this is more general then Fermat's Last Theorem.
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174 + 215 = 235
Lol you don't get it, do you?
So far nobody on earth has got it...
Isn't it better eat some pizza than to just look at it?
Especially if one of the bites might get you pizza for life.
Nice problem.. I would love to win that million! I would be a millionaire on my 15th, which would keep me from having to work 9-5 to make a couple cents.
What! You are only 14 years old? I thought you are about 40 or 50 years old with the pizza restaurant. ROFL
I'm 15 and do not own a pizza restaurant. I wonder what made you think I were
Maybe I was just seeing 30 years in the fututre. lol