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

quadcub.jpgK  =  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

amicable.jpgAMICABLE NUMBERS.

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

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

DOWNLOAD:

least.zip

17/04/2010

QUADRATIC CONGRUENCE

resnonre.jpgQUADRATIC 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

order.jpgORDER 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.jpgSOPHIE 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.jpgCONTINUED 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

deserts.jpgPRIME 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)

sqrt2.jpgFRACTIONS 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

pidigits.jpgPI DIGITS.

THE PROGRAM CALCULATES THE DIGITS OF PI.

DOWNLOAD:

pidigits.zip

07/04/2010

DIOPHANTINE EQUATION

dioph.jpgDIOPHANTINE EQUATION:

Ax + By = C

A,B,C,x,y  POSITIVE INTEGERS.

DOWNLOAD:

dioph.zip

06/04/2010

QUADRATIC RESIDUES

quaresp.jpgQUADRATIC 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

polygenpri.jpgSTUDY 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

pasctriang.jpgPASCAL TRIANGLE.

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

DOWNLOAD:

pasctriang.zip

03/04/2010

PRIMALITY TEST

test.jpgPRIMALITY TEST.

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

DOWNLOAD:

test.zip

02/04/2010

NEXTPRIME

nextprime.jpgNEXTPRIME.

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

DOWNLOAD:

nextprime.zip

DIVISORS

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

DOWNLOAD:

divisors.zip

01/04/2010

PRIME NUMBERS

crible.jpgPRIME NUMBERS IN A RANGE.

DOWNLOAD:

crible.zip

31/03/2010

PRIME FACTORS

primfact.jpgPRIME FACTORS OF AN INTEGER.

DOWNLOAD:

primfact.zip

29/03/2010

PYTHAGOREAN TRIPLES

pytriples.jpgPythagorean 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.jpgCOLLATZ 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

twinprimes.jpgTWIN PRIME PAIRS.

DOWNLOAD:

twinprimes.zip

Goldbach's conjecture

goldbach.jpgGOLDBACH 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.

DOWNLOAD:

goldbach.zip

 

N = X^2 + Y^2

x^2+y^2.jpgTHE PROGRAM SOLVES  N = X^2 + Y^2 (N,X,Y INTEGERS).

DOWNLOAD:

n = x^2 + y^2.zip

MODPOW: A^B MODULO C

modpow.jpgMODPOW. THE PROGRAM CALCULATES  A^B MODULO C.

DOWNLOAD:

modpow.zip

FIBONACCI NUMBERS

fibonacci.jpgTHE PROGRAM CALCULATES FIBONACCI NUMBERS:

DOWNLOAD:

fibonacci.zip

13/04/2009

NUMBER THEORY CALCULATOR

 

2009-04-13_184649.jpgNUMBER THEORY CALCULATOR. UPDATED VERSION.

THE PROGRAM IS FREEWARE.

YOU CAN DOWNLOAD HERE:

(right click on the mouse and "save target as" or "save file as") :

nutecalc1.zip

 

YOU CAN ALSO DOWNLOAD 103 FREEWARE MATH PROGRAMS ON THE SITE:

http://giuseppemerlino.blogspot.com/

GIUSEPPE MERLINO

e-mail   bardesane1947@libero.it

 

acamod0.ico

03/04/2009

NUMBER THEORY CALCULATOR

 

Number theory calculator.jpg

GIUSEPPE MERLINO  e-mail bardesane1947@libero.it

THE CALCULATOR SUPPORTS MAX. 8 DIGITS NUMBERS. THE FUNCTION  A^2 = x^2 + y^2 BECOME VERY SLOW FOR NUMBER WITH MORE THAN FOUR DIGITS.

THE PROGRAM IS FREEWARE. YOU CAN DOWNLOAD HERE:

nutecalc.zip

 

 

YOU CAN ALSO DOWNLOAD 103 FREEWARE MATH PROGRAMS ON THE SITE:

http://giuseppemerlino.blogspot.com/

 

VB6.ICO

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