NUMBER THEORY CALCULATOR

03/05/2010

NUMBER THEORY FREE PROGRAMS

NUMBER THEORY FREE PROGRAMS FOR WINDOWS.

LANGUAGE: ENGLISH.

AUTHOR: GIUSEPPE MERLINO.

IF YOU CLICK ON THE PROGRAM NAME IN THE LEFT COLUMN, YOU WILL FIND THE SCREENSHOT AND THE DOWNLOAD LINK FOR THE INDIVIDUAL PROGRAM.

HERE THERE IS THE ZIP FILE WITH THE FIRST 27 PROGRAMS:

number theory programs.zip

MIRROR 1 :

http://www.freewarefiles.com/program_16_233_57801.html

MIRROR 2 :

http://www.softpedia.com/progMoreBy/Publisher-Giuseppe-Me...

MIRROR 3 :

http://sites.google.com/site/elementarynumbertheory/

MIRROR 4 (alternative direct download link) :

http://sites.google.com/site/elementarynumbertheory/numbe...

The programs are certified free of viruses by Softpedia:

http://www.softpedia.com/progClean/Number-Theory-Clean-15...

21/04/2010

MORDELL'S EQUATION: K = A² - B³

K = A² - B³ (MORDELL'S EQUATION)

The program finds the solutions of the equation K = A² - B³ with K,A,B integers.

DOWNLOAD:

quadcub.zip

20/04/2010

Amicable numbers are two different numbers so related that the sum of the proper divisors of one of the numbers is equal to the other. (A proper divisor of a number is a positive integer divisor other than the number itself).

DOWNLOAD:

amicable.zip

ALIQUOT SEQUENCES

An aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term.
There are 5 cases:
1) The sequence ends with 1.
2) The sequence ends with the starting number and then repeats (Sociable Numbers).
3) The sequence is made by only two numbers (Amicable Numbers).
4) The sequence is made by only one number (Perfect Number).
5) Some numbers have an aliquot sequence which is eventually periodic, but the number itself is not perfect, amicable, or sociable (ex. 95).

DOWNLOAD:

aliquot.zip

19/04/2010

LEAST QUADRATIC NON RESIDUE AND LEAST PRIMITIVE ROOT

LEAST QUADRATIC NON RESIDUE AND LEAST PRIMITIVE ROOT OF A PRIME NUMBER.

DOWNLOAD:

least.zip

17/04/2010

QUADRATIC CONGRUENCE

QUADRATIC CONGRUENCE.

The program checks if A is quadratic residue or quadratic non-residue of P. If A is quadratic residue of P, the program solves the congruence:
X² ≡ A (modulo P)
Namely the program finds the two X values less than P, such that A is the remainder of dividing X² for P.

DOWNLOAD:

resnonres.zip

ORDER OF A MODULO P

The order of A modulo P (prime number) is the smallest positive R for wich : A^R ≡ 1 (mod. P). Since A^(P-1) ≡ 1 (mod. P) always, it is obvious that, if the order of A is less than (P-1), the order should divide (P-1). If the order of A modulo P is equal to (P-1), then A is a primitive root of P.

[ A^R ≡ 1 (mod. P) means that the rest of the division of A^R divided by P is 1 ]

DOWNLOAD:

order.zip

14/04/2010

SOPHIE GERMAIN NUMBERS

SOPHIE GERMAIN NUMBERS IN A GIVEN RANGE.

A PRIME NUMBER P IS A SOPHIE GERMAIN PRIME IF 2P + 1 IS ALSO PRIME.

DOWNLOAD:

sophie.zip

12/04/2010

CONTINUED FRATION OF A SQUARE ROOT

$cfrac.jpg$ CONTINUED FRACTION OF A SQUARE ROOT.

THE SQUARE ROOT OF A SQUAREFREE INTEGER HAS A PERIODIC CONTINUED FRACTION OF THE FORM:

a0, a1, a2, a3, a4...........a2, a1, 2a0

DOWNLOAD:

cfrac.zip

PRIME DESERTS

PRIME DESERTS.

THE PROGRAM FINDS THE LARGEST INTERVAL OF CONSECUTIVE NON-PRIMES IN A GIVEN RANGE A - B.

DOWNLOAD:

desert.zip

11/04/2010

FRACTIONS GENERATING SQRT(2)

FRACTIONS GENERATING SQRT(2).

START WITH 1/1 , THEN FROM EACH FRACTION A/B , THE FOLLOWING WILL BE (A + 2B)/(A + B).

DOWNLOAD:

sqrt2.zip

09/04/2010

PI DIGITS

PI DIGITS.

THE PROGRAM CALCULATES THE DIGITS OF PI.

DOWNLOAD:

pidigits.zip

07/04/2010

DIOPHANTINE EQUATION

DIOPHANTINE EQUATION:

Ax + By = C

A,B,C,x,y POSITIVE INTEGERS.

DOWNLOAD:

dioph.zip

06/04/2010

QUADRATIC RESIDUES

QUADRATIC RESIDUES OF A PRIME NUMBER.

A quadratic residue of a prime number is the remainder of the division of a perfect square for the prime number. All prime numbers have (p-1) / 2 quadratic residues and (p-1) / 2 quadratic non residues.

DOWNLOAD:

quaresp.zip

CLEAR BEFORE A NEW CALCULATION !

05/04/2010

X^2 - X + 41

STUDY OF THE POLYNOMIAL X^2 - X + 41

THE POLYNOMIAL X^2 - X + 41 GENERATES 40 CONSECUTIVE PRIMES FROM X = 1 TO X = 40. THE PROGRAM CALCULATES THE NUMBER OF PRIMES GENERATED BY THIS POLYNOMIAL IN A GIVEN RANGE.

DOWNLOAD:

polygenpri.zip

04/04/2010

PASCAL TRIANGLE

PASCAL TRIANGLE.

THE PROGRAM DISPLAYS THE N-TH ROW OF PASCAL'S TRIANGLE.

DOWNLOAD:

pasctriang.zip

03/04/2010

PRIMALITY TEST

PRIMALITY TEST.

THE PROGRAM CHECKS WHETHER AN INTEGER IS A PRIME NUMBER OR NOT.

DOWNLOAD:

test.zip

02/04/2010

NEXTPRIME

NEXTPRIME.

THE PROGRAM FINDS THE SMALLEST PRIME NUMBER GREATER THAN A GIVEN NUMBER.

DOWNLOAD:

nextprime.zip

DIVISORS

THE PROGRAM CALCULATES THE PROPER DIVISORS OF A NUMBER, THEIR SUM AND THEIR NUMBER.

DOWNLOAD:

divisors.zip

01/04/2010

PRIME NUMBERS

PRIME NUMBERS IN A RANGE.

DOWNLOAD:

crible.zip

31/03/2010

PRIME FACTORS

PRIME FACTORS OF AN INTEGER.

DOWNLOAD:

primfact.zip

29/03/2010

PYTHAGOREAN TRIPLES

Pythagorean triple: consists of three positive integers A, B, and C, such that A² = B² + C².
Euclid's formula is a fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers M and N with M > N. The formula states that the integers:

A = M² + N²
B = M² - N²
C = 2*M*N

form a Pythagorean triple.

DOWNLOAD:

pytriples.zip

28/03/2010

COLLATZ CONJECTURE

COLLATZ CONJECTURE:

Take any natural number n. If n is even, divide it by 2 to get n / 2, if n is odd multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1.

DOWNLOAD:

collatz.zip

TWIN PRIME PAIRS

TWIN PRIME PAIRS.

DOWNLOAD:

twinprimes.zip

Goldbach's conjecture

GOLDBACH CONJECTURE: is one of the oldest unsolved problems in Number Theory. It states: every even number greater than 2 can be expressed as the sum of two primes.