number-theory | 易学教程

Converting a number to base 64

阅读更多关于 Converting a number to base 64

问题 So I am trying to program (in Python 3 without strings) this cool project that I found. Return the 6-character string representation of the 36-bit number n as a base-64 number in reverse order where the order of the 64 numerals is: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-+ For example, encode(0) → '000000' encode(9876543210) → 'gR1iC9' encode(68719476735) → '++++++' What I have so far is: def encode(n): SYM = {'0': 0, '1': 1, '2': 2, '3': 3, '4': 4, '5': 5, '6': 6, '7':

Factorization of an integer

阅读更多关于 Factorization of an integer

While answering another, I stumbled over the question how I actually could find all factors of an integer number without the Symbolic Math Toolbox . For example: factor(60) returns: 2 2 3 5 unique(factor(60)) would therefore return all prime-factors, "1" missing. 2 3 5 And I'm looking for a function which would return all factors ( 1 and the number itself are not important, but they would be nice) Intended output for x = 60 : 1 2 3 4 5 6 10 12 15 20 30 60 I came up with that rather bulky solution, apart from that it probably could be vectorized, isn't there any elegant solution? x = 60; P =

How does this prime number test in Java work?

阅读更多关于 How does this prime number test in Java work?

问题 The code snippet below checks whether a given number is a prime number. Can someone explain to me why this works? This code was on a study guide given to us for a Java exam. public static void main(String[] args) { int j = 2; int result = 0; int number = 0; Scanner reader = new Scanner(System.in); System.out.println("Please enter a number: "); number = reader.nextInt(); while (j <= number / 2) { if (number % j == 0) { result = 1; } j++; } if (result == 1) { System.out.println("Number: " +

finding a^b^c^… mod m

阅读更多关于 finding a^b^c^… mod m

I would like to calculate: a b c d . . . mod m Do you know any efficient way since this number is too big but a , b , c , ... and m fit in a simple 32-bit int. Any Ideas? Caveat: This question is different from finding a b mod m. Also please note that a b c is not the same as (a b ) c . The later is equal to a bc . Exponentiation is right-associative. Tacet The answer does not contain full formal mathematical proof of correctness. I assumed that it is unnecessary here. Besides, it would be very illegible on SO, (no MathJax for example). I will use (just a little bit) specific prime

Parallel Algorithms for Generating Prime Numbers (possibly using Hadoop's map reduce)

阅读更多关于 Parallel Algorithms for Generating Prime Numbers (possibly using Hadoop's map reduce)

Generating Prime numbers is a toy problem that I often attempt from time to time, especially when experimenting with a new programming language, platform or style. I was thinking of attempting to write a Prime Number Generation algorithm or a Prime Number Test Algorithm using Hadoop (Map Reduce). I thought I'd post this question to get tips, references, to algorithms, approaches. Although my primary interest is a Map Reduce based algorithm I wouldn't mind looking at new Hadoop programming models or for example looking at using PiCloud I have seems some interesting questions here on Prime

finding a^b^c^… mod m

阅读更多关于 finding a^b^c^… mod m

问题 I would like to calculate: a b c d . . . mod m Do you know any efficient way since this number is too big but a , b , c , ... and m fit in a simple 32-bit int. Any Ideas? Caveat: This question is different from finding a b mod m. Also please note that a b c is not the same as (a b ) c . The later is equal to a bc . Exponentiation is right-associative. 回答1: The answer does not contain full formal mathematical proof of correctness. I assumed that it is unnecessary here. Besides, it would be

Parallel Algorithms for Generating Prime Numbers (possibly using Hadoop's map reduce)

阅读更多关于 Parallel Algorithms for Generating Prime Numbers (possibly using Hadoop's map reduce)

问题 Generating Prime numbers is a toy problem that I often attempt from time to time, especially when experimenting with a new programming language, platform or style. I was thinking of attempting to write a Prime Number Generation algorithm or a Prime Number Test Algorithm using Hadoop (Map Reduce). I thought I'd post this question to get tips, references, to algorithms, approaches. Although my primary interest is a Map Reduce based algorithm I wouldn't mind looking at new Hadoop programming