This is really just an exercise in algebra.

And here is Gauss' trick, for observation, which is that the result of the third recursive call minus each of the first two what happens.

That crosses out. a squared minus a squared crosses out. a to the third, it'll all cross out.

Let's see, this z plus 2 cancels out with this z plus 2.

We have a positive 2 and a minus 2.

8 is 2 to the third.

Let me erase some of this.

Well, we take the exponent, multiply it by the expression.

The left hand side, we're just left with the 3x.

Ok this is been written with our pen.

Subtract 49 from both sides.

Then times 5 times 4 times 3 times 2 times 1.

So that's 6.

Well, a to the first, minus a to the first.

hung on a cross with nails.

Well, that just equals 1 3 again.

Negative 1 3 times 6z is going to be minus 2z.

The rain is beating against the window.

that's equal to x minus f squared plus y squared.

We know that f of 2 is 8. 2 3 is 8

But the best thing, I'm guessing, is to just factor these out and all sorts of things will start canceling out with each other.

Now, Alice ads her private colour to Bob's mixture.

You horsewhipped the woman he loves.

And already it looks like there's some cancellation that we can do.

Multiplying this out misses exactly 1 term, pXi, which is number 3.

And that's why I put the 1 2 there.

But this is equal to a squared minus b squared, because the middle terms cancel out.

2x minus 5 is equal negative 11 let's add 5 to both sides of this equiation.

If you wanted to solve it algebraically you could add 11x to both sides and both of these terms will cancel out with each other and all you would be left with is a 4 is equal to a negative 11, which is not possible for any x that you pick.

Negative.

The rain is beating against the windows.

I have to conquer this!

Is that any way for two old friends... to do business?

And they don't always work together.

And then your right hand side, once again, distribute the x. x times 2 is 2x. x times 15 x, well, x times something over x is just going to be the something. x times 15 x is just going to be 15 plus 15.

Meaning d should be Alice's private key.

He accidentally hit his thumb with the hammer.

This is a PX17 drive. It's got an autoerase function.

You can add x squared to both sides to get rid of this and this.

It's about living.

But just a second later, most matter and all of the antimatter had destroyed one another, producing an enormous amount of radiation that can still be observed today.

Want to talk about it?

So you've effectively negated 60 years of aeronautic research.

So that's going to be equal to 6y squared minus x squared plus 3.

It's wonderful.