Texas zillionaire* Andrew Beal is a self-taught math enthusiast. He has offered a one-million dollar prize to anyone who can prove his “Beal Conjecture”. Mathematicians have been at it since the 1980s — but to this point, nobody has had any luck.
Surely a prize that large on a problem that old must be difficult to understand, right?! Well…not exactly. It’s pretty straightforward algebra. Proving the conjecture is not straightforward, but understanding it is.
See the problem here: http://newsfeed.time.com/2013/06/11/solve-this-math-problem-win-a-million-bucks/
BADGING: Read the article linked above. Then read the rules/procedures for submitting a solution: http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize-rules Why do you think the American Mathematical Society will not accept manuscripts directly, but instead require that the solution be published in a journal? Answer in a complete sentence or two.
To complete your badge, answer the following Questions:
- One example solution of the Beal Conjecture is 34^5 + 51^4 = 85^4. What common prime factor do all of the bases (A, B, and C, in the Beal Conjecture) share?
2) How would you complete this statement using the Beal Conjecture: 3^3 + 6^3 = __________ (Don’t give the answer as a counting number, express it in its “Beal Conjecture Form”
3) 19^4 + 38^3 leads to a Beal Conjecture solution. Without actually evaluating either of those exponential terms, tell me what you must know about the number C in The Beal Conjecture: 19^4 + 38^3 = C^z
*there are no such things as zillionaires. Mr. Beal has a net worth of 11 billion US Dollars.