thebadbyte.com

The Bad Byte

Wednesday, August 12, 2015. A Beauty Pageant for Mathematicians. Lots of people like to look at sports statistics. Some people like to look at football statistics, others like to analyze baseball statistics, and I like to analyze statistics from the International Mathematics Olympiad (IMO) in my spare time. IMO stats offer a peek into a country’s education system, and its ability to utilize its human resources. The American economy can't afford a better education system. Only 3 were women. Which is a cou...

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Wednesday, August 12, 2015. A Beauty Pageant for Mathematicians. Lots of people like to look at sports statistics. Some people like to look at football statistics, others like to analyze baseball statistics, and I like to analyze statistics from the International Mathematics Olympiad (IMO) in my spare time. IMO stats offer a peek into a country’s education system, and its ability to utilize its human resources. The American economy can't afford a better education system. Only 3 were women. Which is a cou...

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The Bad Byte | thebadbyte.com Reviews

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Wednesday, August 12, 2015. A Beauty Pageant for Mathematicians. Lots of people like to look at sports statistics. Some people like to look at football statistics, others like to analyze baseball statistics, and I like to analyze statistics from the International Mathematics Olympiad (IMO) in my spare time. IMO stats offer a peek into a country’s education system, and its ability to utilize its human resources. The American economy can't afford a better education system. Only 3 were women. Which is a cou...

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thebadbyte.com

1

The Bad Byte: How To Get To Buzludzha

http://www.thebadbyte.com/2015/06/how-to-get-to-buzludzha.html

How To Get To Buzludzha. The old communist building at Buzludzha captured the imagination of people around the world after being featured in several lists of cool abandoned buildings. I went there the other day and I encountered things that I felt the need to share publicly. It takes approximately 3 hours to drive there from either end of Bulgaria and the drive itself is an adventure in a league of its own. You need to get to Gabrovo first. There is a paved road up to the very top of Buzludzha. According...

2

The Bad Byte: Finding Phi

http://www.thebadbyte.com/2014/11/finding-phi.html

Euler's phi function, namely φ(n), pops up in many odd places. Φ(n) is always even. Φ(n) is the number of integers smaller than n that are relatively prime, or coprime. From Elementary Number Theory. By Kenneth H. Rosen.]. If n is the product of two distinct primes p and q, then. Proof: If n is the product of two distinct primes p and q then. Because for any prime p its greatest common divisor GCD. Φ(q) = (p-1)(q-1) =. Is it possible to find. Φ(n) without factoring n to find the values of p and q? Euler ...

3

The Bad Byte: Life of Phi

http://www.thebadbyte.com/2015/01/life-of-phi.html

In last years' Finding Phi post I presented an algorithm for finding the order of 2 mod n. It is not a particularly fast one so I thought I'd modify it based on a few very basic observations about the structure of the row at 2 in exponentiation tables of Z. For n 2 where n is the product of two distinct primes greater than 2:. The row at 2 is a sequence 2. Where every subsequent entry n is equal to the previous one times 2, or in other words:. At any index if a. A few "unresponsive script" nudges in the ...

4

The Bad Byte: Varna Necropolis

http://www.thebadbyte.com/2015/07/varna-eneolithic-necropolis.html

Last year at a developers' conference in San Francisco my husband and I met a man who bragged about how he visited every continent. When I asked him where the oldest processed golden artifacts were discovered he was quick to point to Egypt. My husband in front of the Archeological Museum in Varna. Golden earrings with the goddess of victory 5th century B.C. In a number of graves found in the area of present day Varna, there were thousands of intricate gold artifacts. Looked at in isolation from other art...

5

The Bad Byte: Finding Phi Even Faster

http://www.thebadbyte.com/2015/07/finding-phi-even-faster.html

Finding Phi Even Faster. Phi(n) is the number of integers that are coprime with n; phi(n) = (p-1)(q-1) when n is the product of two distinct odd primes p and q. In Types of Exponents. I showed that phi(n)/2 is a universal exponent when n is the product of two distinct odd primes. In Life of Phi. I came up with one way of finding the order of 2 mod n when n is the product of two distinct odd primes, and then I used it in Finding Phi Faster. A few days ago I uncovered a new way. Var cycle length = find ord...

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Wednesday, August 12, 2015. A Beauty Pageant for Mathematicians. Lots of people like to look at sports statistics. Some people like to look at football statistics, others like to analyze baseball statistics, and I like to analyze statistics from the International Mathematics Olympiad (IMO) in my spare time. IMO stats offer a peek into a country’s education system, and its ability to utilize its human resources. The American economy can't afford a better education system. Only 3 were women. Which is a cou...

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