**Ax + By = Cz.**

Simple algebra, right?

Oh how deceptively innocuous a few elementary variables can seem. You’re actually looking at something inspired by one of the great mysteries of mathematics, known as Fermat’s Last Theorem and named after the 17th century French lawyer and mathematician Pierre de Fermat. Fermat came up with his own theorem back in 1637, scribbling it in the margins of his copy of the Greek text Arithmetica by Diophantus and surmising that — put your math caps on and buckle up — if n were an integer greater than 2, then the equation Xn + Yn = Zn has no positive integral solutions. The note was discovered after Fermat’s death, and it took over 350 years and untold failed attempts by others for someone to prove the theorem. In 1995, British mathematician Andrew Wiles, who’d been fascinated with the theorem since he was a child, finally got the job done, having puzzled over it in secret for roughly six years.

That’s where Texas billionaire D. Andrew Beal comes in. In 1993, he posited a closely related number theory problem hence dubbed Beal’s Conjecture (that first A-B-C equation above), where the only solution is possible when A, B and C have a common numerical factor and the exponents x, y and z are greater than 2. Beal’s been trying to solve his theorem ever since, reports ABC News, offering cash rewards in steadily increasing amounts — $5,000 in 1997, $100,000 in 2000 – to anyone with the knack to get the job done.

The prize total in 2013: $1 million, which is either a sign of Beal’s magnanimity or his skepticism that it’s actually possible. (Since Beal is worth a reported $8 billion, there’s little need to worry about whether he’ll actually pay the winner.)

It’s apparently not just about the money for Beal, either: In a statement, he said “I’d like to inspire young people to pursue math and science. Increasing the prize is a good way to draw attention to mathematics generally … I hope many more young people will find themselves drawn into the wonderful world of mathematics.”

[Update: The challenge is sponsored by the American Mathematical Society; the rules, including where to submit proposed solutions by email or snail mail, are available here.]

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