Another Bridge Strike

I’m at home too, more accurately working from home and clearly procrastinating :blush:
I note CF is posting in the wee small hours of the morning, suggesting he too is probably not overburdened with work today.

Clearly CF has boundless confidence in his own mathematical abilities, and time to spare, so here’s something that is worth him spending time on, it is allegedly worth $1,000,000 if it can be proved correct - shouldn’t take more than an afternoon for someone with CF’s ability :laughing: The Beal conjecture

[sciencealert.com/6-simple-m ... -can-solve](https://www.sciencealert.com/6-simple-maths-problem-that-no-one-can-solve)

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…