Which is your most favourite number.

The smallest integer with three distinct integer cubes cannot be found, unless one wishes to call it - (aleph null), I suppose.

Cubing a negative integer produces ... a negative integer. So if we cube three distinct negative integers, and then add the cubes, we get a negative integer smaller than any of the three cubes. And since we can continue to pick ever smaller distinct negative integers to cube, the process seems to be endless.

I asked AI for the smallest integer that is the sum of the cubes of three distinct integers (before I had bothered to first think it through) and AI babbled on and on, repeating itself, throwing out a lot of irrelevant observations, and never coming to a conclusion that it didn't acknowledge was incorrect.

It was rather funny and cheered me right up.

The simple AI apparently has to mine its answers from the internet, and so throws out a lot of things that simply don't help and don't pertain. It didn't really seem to "reason" effectively on its own, at least in this context.

I'm sure there are more specialized, expensive AIs that would do better. At least I hope so.

While babbling, the AI DID mention 1729 -- which, though ultimately unhelpful in this context, IS a very interesting number in its own right, as most math addicts with an old school education will probably recognize. At least if they know who Ramanujan and Hardy were -- and that seems quite likely.

I'm curious how many of the readers will recognize instantly (that is, from memory) why it is interesting.

Mines 67

@Anonymous_IIII said ^

Mines 67

breh

@Chesslayer12 said ^

I half expected someone to say, "mY FaVoRItE NuMBer iS SiX-SeVEn".

@Anonymous_IIII said ^

Mines 67

self-fulfilling prophecy

7 as well. Bc of Ronaldo and how like anything that happens to me that involves a 7 is always good.

@Anonymous_IIII said ^

Mines 67

Bro.

@Anonymous_IIII said ^

Mines 67

brotha

I love63

I know this is an irrational choice, but I like the square root of 2.