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Aaron N. Tubbs

Dragon chaser.

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So I’m working on my 100th Project Euler problem. Out pops a Diophantine equation I don’t particularly want to solve. So, I toss it into Wolfram Alpha. I was thinking this was one of those taylor-made problems; whereas most of my queries result in lost results, this is a pretty straightforward request. Granted, I’m asking the Mathematica engine to take a leap and realize I want my equation treated as a Diophantine equation, and not a continuous equation, but I try my luck, punching in:

2b**2-2b-n**2+n=0

Gah. I do get a continuous plot (sort of expected this; I didn’t find the graphing part of graphing calculators useful 15 years ago, and I still don’t), and several alternative ways of writing it. I also get, lo and behold, a relatively straightforward solution in terms of n, and a horribly complicated solution in terms of b, even though Alpha recognizes that the solution set I’m looking for is in the set Z (integers).

Okay, no problem. I’ll just hint it a bit, and instruct Alpha that I’m working with a Diophantine equation, and I want a simple solution. So I search for “Diophantine” on Alpha, and it can’t find anything.

Really?

There’s a ton of shit about Diophantine equations on Wolfram’s own Math World. But for some reason, Alpha is not aware of this fact.

Sigh.

So I go through the Mathematica documentation, and get sidetracked with some toys to play with, like:

FindInstance[2b**2-2b-n**2+n=0,{b,n}]

Of course, Alpha is not just a free version of web Mathematica, so it just sort of throws up on this and suggests something else, which ultimately recursively leads me back to my original search result.

All I wanted was some generating functions, but that’s probably too much to ask.

Whatever, I’m immortal now, suck it.