Bay 12 Games Forum

Especially since Ewadd will not be directly providing us tribute or taxes, and given we very specifically refrained from looting the surrounding area, we should probably keep going so we can actually get some material compensation.

A

At the upper end, a dumb storage of every single possible position[1] vector-multiplied with every possible ruleset[2] wouldn't technically need to be AIed

More than atoms in the universe. Good luck storing that.

By that I mean, is there a natural number b such that a³ - b² = b+1 and (b+1)² - a³ = b, or alternatively, a³ - (b+1)² = b and b² - a³ = (b+1)? Let's call the first set of conditions H, and the alternative set of conditions G.

Very interesting question. I'd like to see the python code too, mine was rubbish and chugged the laptop hard when checking a up to 10,000.

Had a look at this but haven't made much progress on the why of it. I'm not a number theorist though. Here's a few things:

Facts about squares tell us that the first part of H is enough, i.e. a^3 = b^2 + b + 1 means that a^3 + b is (b+1)^2.

Wolfram gave me 4 integer solutions for a^3 - b^2 - b - 1 = 0 , but the other 3 rely on negative or 0 a or b.

I think you can just reformulate the problem as: 4 a^3 = k^2 +3 for some integers a,k, but I don't know why that only has the 4 integer solutions.

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You're right that G is impossible for positive integer a and b. There's a nice way of seeing why:

suppose G holds for some integer a, b

Then a^3 = b (b+1)

b and b+1 share no common factors... so must be cubes of integers themselves, as otherwise a would not be a cube.

The only integer cubes with a difference of 1 are -1, 0 and 1. So we obtain b=0 or b+1 = 0, so a=0 and b=-1 or b=0

Would love to see other people chime in on this, but I'd advise you to check if it's a case of an unsolved problem in number theory before getting too invested. There's a lot of those, and some can be stated very simply.

There was the sound of the very air tearing as Mildred forcibly slowed her charge with powerful counter winds, her missed attack leaving a furrow in the dirt. By the time she was reoriented, Akihiko had caught up and was already attacking back, hitting her with a kick that she couldn't fully block in time. Her forearm and shoulder took the majority of the blow and she let herself roll with it, cartwheeling wildly through the air and letting the momentum play itself out while rising up out of reach before stopping herself. She floated upside down in space for a moment, considering her plan, then corkscrewed around and moved in again.

As she dived down toward Akihiko, her body became alight with bluish-white fire, which she channeled into her fist for a powerful Superman-style punch.

Dyshidrosis seems to be beginning to clear up. It was a horrific outbreak. Left hand's gotten itchy now but only on one finger, and my right's not itching at all now and is just dry in the aftermath.

I did have a large enough blister on my left hand that I had to pop it. Thankfully it was painless.

Swapped > and = around, so that down stairs are no longer stockpiles and stockpiles are no longer down stairs. If anyone wants a pre-fixed mini version. It was a quick swap with GIMP, but I believe I managed to keep the alignment.

Discovered just how badly I'm being ripped off by Burger King. The difference between Value and Medium is measurable in millimeters, not even enough for a single goddamn fry. And that was after they spilled and threw out a few of my fries when moving my order from a tray to a bag after specifically telling them when I placed the order it was to go(the cashiers are supposed to ask).

Instead of the classic tributary system, you offer a "subsidiary alliance". As you expose your conditions, most grow increasingly curious, while a few ones get livid as they fear for the autonomy of the city.
After you end your speech, a quick debate happens amongst the envoys.

Diplomatic roll: 1D20 - 2 (power balance) - 2 (apparently reasonable offer) = 1! (Critical Success) (twice in a row, you lucky boys)

The few skepticals are quickly shunned by the others, too mesmerized by the possibilities offered to them. They enthusiastically thank you and promise bringing your offer to the city’s council.

What is said is done, and a formal agreement is pronounced two days later. Officials will deal with the details.

However, this rise another question: will you march up towards Nenubilanur or consider the campaign done?

A) Nenubilanur will pay!
B) Ewadd is a fair enough reward. We shall stop there.

Some people have Cyanophobia. Replace all blue pixels with spiders.