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The Collatz conjecture is one of the most famous unsolved mathematical problems, because it's so simple, you can explain it to a primary-schoolaged kid, and they'll probably be intrigued enough to try and find the answer for themselves. So here's how it goes: pick a number, any number. If it's even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat those steps again with your new number. Eventually, if you keep going, you'll eventually end up at 1 every single time (try it for yourself, we'll wait). As simple as it sounds, it actually works. But the problem is that even though mathematicians have shown this is the case with millions of numbers, they haven't found any numbers out there that won't stick to the rules. "It's possible that there's some really big number that goes to infinity instead, or maybe a number that gets stuck in a loop and never reaches 1," explains Thompson. "But no one has ever been able to prove that for certain." The Beal conjecture The Beal conjecture basically goes like this... If Ax + By = Cz And A, B, C, x, y, and z are all positive integers (whole numbers greater than 0), then A, B, and C should all have a common prime factor. A common prime factor means that each of the numbers needs to be divisible by the same prime number. So 15, 10, and 5 all have a common prime factor of 5 (they're all divisible by the prime number 5). So far, so simple, and it looks like something you would have solved in high school algebra. But here's the problem. Mathematicians haven't ever been able to solve the Beale conjecture, with x, y, and z all being greater than 2. For example, let's use our numbers with the common prime factor of 5 from before.... 51 + 101 = 151 but 52 + 102 ≠ 152 There's currently a US$1 million prize on offer for anyone who can offer a peer-reviewed proof of this conjecture... so get calculating.