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Crazy Math

Friday, February 12, 2010. More on "Hasse Interrogation". I realized that I'd sort of buried the lede in my post below about what I called "Hasse Interrogation". The idea is pretty elementary and I'm kind of surprised it hasn't popped up in the usual places (I've been searching the literature, web, asking around, etc for a few months now). Here are the basics:. We know a few things about x and y, but those things aren't particularly useful for finding all of the solutions to the equation. For instanc...

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Friday, February 12, 2010. More on Hasse Interrogation. I realized that I'd sort of buried the lede in my post below about what I called Hasse Interrogation. The idea is pretty elementary and I'm kind of surprised it hasn't popped up in the usual places (I've been searching the literature, web, asking around, etc for a few months now). Here are the basics:. We know a few things about x and y, but those things aren't particularly useful for finding all of the solutions to the equation. For instanc...
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1 crazy math
2 and so on
3 simplify
4 primality
5 goldbach
6 which means
7 hasse and hensel
8 hasse interrogation
9 6 no solutions
10 7 no solutions
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Crazy Math | crazymath.blogspot.com Reviews

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Friday, February 12, 2010. More on "Hasse Interrogation". I realized that I'd sort of buried the lede in my post below about what I called "Hasse Interrogation". The idea is pretty elementary and I'm kind of surprised it hasn't popped up in the usual places (I've been searching the literature, web, asking around, etc for a few months now). Here are the basics:. We know a few things about x and y, but those things aren't particularly useful for finding all of the solutions to the equation. For instanc...

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Crazy Math: Figurate numbers and factoring, a gentle intro

http://crazymath.blogspot.com/2008/12/figurate-numbers-and-factoring-gentle.html

Tuesday, December 09, 2008. Figurate numbers and factoring, a gentle intro. Ok, back to factoring. Chances are you're familiar with at least one set of figurate numbers - the squares:. The sequence of squares can be generated very easily through addition; simply add up x number of odd numbers (starting with 1) to find x 2:. There are many other "kinds" of figurate numbers, but they all have the same simple rule for generating them. Here are a couple of examples:. 22 = 1 4 7 10. X 2 = y 2 mod N. In this c...

2

Crazy Math: July 2004

http://crazymath.blogspot.com/2004_07_01_archive.html

Thursday, July 15, 2004. Fractals, Fractals everywhere. I wanted to be doubly sure I understood the definition of a fractal before I posted this, so I've been doing some research into fractals. More specifically, I've been looking at fractal sequences, and I think I'm sure enough about the definition of fractal sequences to state the following:. Let Z = all positive integers greater than 0. BigOmega(Z) is a fractal sequence. Posted by Andrew : 4:27 PM 0 comments. Friday, July 09, 2004.

3

Crazy Math: January 2010

http://crazymath.blogspot.com/2010_01_01_archive.html

Friday, January 08, 2010. Thoughts on Goldbach Conjecture. Yeah, and who doesn't have thoughts on the Goldbach Conjecture? It's attracted the gaze of this amateur, and so I'll try to wade into the waters slowly. There's an interesting sequence in the OEIS - A144650. I like it because, when you view it as a triangular array, it makes a nice pattern (click on the link, then click on "tabl" in the "Keyword" section). So what about it? Ok, you might ask, so what's the big deal? The fun part of this is it sug...

4

Crazy Math: November 2009

http://crazymath.blogspot.com/2009_11_01_archive.html

Tuesday, November 24, 2009. Posted by Andrew : 11:24 AM 0 comments. Monday, November 09, 2009. Here's a bit about what I've been working on recently; the concept is something I've been calling "Hasse Interrogation". This is where figurate numbers come in handy - we can take any quadratic of the form x 2 n = y 2 and use the Hasse Principle to see if these equations have rational solutions:. 25c 2 n = y 2. 49d 2 n = y 2. So, imagine that we group digits, like this:. 1 3 5 7 9 11 13 15. The fun part (and th...

5

Crazy Math: June 2004

http://crazymath.blogspot.com/2004_06_01_archive.html

Thursday, June 24, 2004. Here'a a conjecture (my first):. Conjecture: The "length" of a set S(n - x) = the xth member of the Lower Wythoff. Or, in other words, the "length" of S(n - x); x = 1 is 1, x = 2 is 3, x = 3 is 4, x = 4 is 6, x = 5 is 8, and so on. If we add 2 to each member of the Lower Wythoff sequence, we get the absolute length (i.e., the length including the first and last set). Posted by Andrew : 4:51 PM 0 comments. Friday, June 18, 2004. Errors, errors, aren't they fun? We now construct se...

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Crazy Math

Friday, February 12, 2010. More on "Hasse Interrogation". I realized that I'd sort of buried the lede in my post below about what I called "Hasse Interrogation". The idea is pretty elementary and I'm kind of surprised it hasn't popped up in the usual places (I've been searching the literature, web, asking around, etc for a few months now). Here are the basics:. We know a few things about x and y, but those things aren't particularly useful for finding all of the solutions to the equation. For instanc...

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