Hurwitz's theorem (number theory)

Okay, kiddo, let me explain Hurwitz's Theorem to you.

Imagine you have two numbers, let's call them a and b. And you want to multiply them together to get c: c = a x b.

Now, sometimes you can divide c by a and get a whole number, and sometimes you can divide c by b and get a whole number. But sometimes you can't divide c by either a or b and get a whole number.

Hurwitz's Theorem is all about figuring out when you can and can't divide c by a or b to get a whole number.

Here's the rule: if a and b are both irrational numbers (that means they can't be written as a simple fraction like 1/2 or 3/4), then you can't make c into a whole number by dividing it by either a or b.

But if a and b are both rational numbers, (that means they can be written as a simple fraction), then you can always make c into a whole number by dividing it by either a or b.

So, to sum up, Hurwitz's Theorem tells us whether two numbers can be multiplied together to make a whole number, based on whether those numbers are rational or irrational. Pretty cool, huh?