2.3 Euclidean Algorithm

http://users.erols.com/eweidaw/applets/EuclidExtension.html

Contains an applet for the extended Euclidean Algorithm

http://www.math.sc.edu/~sumner/numbertheory/euclidean/euclidean.html

Contains an applet for the extended Euclidean Algorithm and also displays the steps for the algorithm and the LCM

http://www.calvin.edu/~rpruim/courses/m156/mathlets/Euclid/

Contains an applet for the extended Euclidean Algorithm and also displays the steps for the algorithm

http://www.central.edu/homepages/lintont/classes/spring01/cryptography/java/gcd.html

Contains an applet for the Euclidean Algorithm for two or more integers and also returns the LCM

http://www.math.umn.edu/~garrett/js/gcd.html

Contains an applet for the Euclidean Algorithm and also displays the steps

2.4 Linear Diophantine Equations

http://www.thoralf.uwaterloo.ca/htdocs/linear.html

Contains a solver. Solution displays both the Euclidean Algorithm and the back substitutions, with a particular solution and the general solution.

http://www.kolumbus.fi/hoijer.heikki/ (Scroll to #3)

Contains a solver. Solution displays, with comments, both the Euclidean Algorithm and the back substitutions, with a particular solution and the general solution. (You can scroll to the start of the solution with the up arrow.)

http://www.student.math.uwaterloo.ca/~madrewbr/lde.html

Contains a solver -- just a black box.

3.1 Fundamental Theorem of Arithmetic

http://www.math.umn.edu/~garrett/crypto/a01/NaivePrimalityTester.html

Tests primality of individual numbers up to 18 digits.

http://www.2357.a‑tu.net/index.php?link=Primality

Tests primality of individual numbers and gives factorization of composites. For the range of numbers testable, see the result format information below the applet. “Clear” clears only the entry window; you need to clear the output window manually by highlighting and deleting.

http://www.cryptographic.co.uk/factorise.html

Here you can test individual numbers or a range of numbers. Read the instructions. Results include factorizations.

3.2 Sieve of Eratosthenes

http://ccins.camosun.bc.ca/~jbritton/jberatosapplet.htm

A visual display of the sieve for 1 to n, with a maximum n of 200.

http://www.math.utah.edu/~alfeld/Eratosthenes.html

Displays the pattern of location of primes in sieves of varying sizes. Read the instructions.

http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm

Interactive sieve 1 to 400.

4.2 Basic Properties of Congruence

http://www.cs.usask.ca/resources/tutorials/csconcepts/numbertheory/tutorial/trail/tp03.html

Calculates least residue mod n.

http://math.uh.edu/~minru/web/cong1.html

Congruence classes mod n. See also the same address with “1" replaced by 2, 3, or 4.

http://ccins.camosun.bc.ca/~jbritton/jbmodart.htm

Tables for +, -, *, / mod n (The rest of the site relates such tables to artistic patterns.)

http://www.cut‑the‑knot.com/blue/Modulo.shtml

Tables for +, -, *, / mod n

4.3 Special Divisibility Tests

http://www.math.niu.edu/~apel/applets/numericalAnalysis/base/baseConversion/

Converts base b to base 10.

http://www.stormloader.com/ajy/baseconv.html

Converts from base b to base b’

http://www.comsc.ucok.edu/~pcarter/applet/BaseConvApplet.html

Converts between binary, octal, decimal, hexadecimal

4.4 Linear Congruences

http://math.uh.edu/~minru/web/lincong3.html

Solves linear congruence ax / b mod n

http://math.uh.edu/~minru/web/chinese3.html

Solve systems of linear congruences. See also the same address with “3" replaced by 1, 2, or 4.

5.3 The Little Theorem

http://www.math.fau.edu/Richman/carm.htm

Tests for primality using Fermat’s Little Theorem

6.1 The Functions J and F & 6.2 The Moebius Inversion Formula

http://www.alpertron.com.ar/ECM.HTM

Returns J (n), F (n), N (n), µ (n)

6.4 An Application to the Calendar

http://www.mste.uiuc.edu/activity/zeller/

Calculates day of week for given date

7.2 Euler’s Phi Function

http://www.alpertron.com.ar/ECM.HTM

Returns J (n), F (n), N (n), µ (n)

7.5 An Application to Cryptography

http://cisnet.baruch.cuny.edu/holowczak/classes/9444/rsademo/

Discussion and demo of RSA algorithm.

8.1 The Order of an Integer Modulo n

http://www.math‑it.de/Mathematik/Zahlentheorie/OrdnungWert.html

Computes the order

http://math.uh.edu/~minru/web/orders1.html

Computes as many powers of a number as you want.

10.2 The Search for Perfect Numbers

http://math.uh.edu/~minru/web/special2.html

Tests whether a number is perfect and generates lists of perfect numbers.

10.3 Mersenne Primes

http://math.uh.edu/~minru/web/special2.html

Tests whether a Mersenne number is prime.

10.4 Fermat Numbers

http://math.uh.edu/~minru/web/special3.html

Tests whether a Fermat number is prime

11.1 Pythagorean Triples

http://math.uh.edu/~minru/web/represent4.html

Generates Pythagorean triples with x and y less than a fixed bound. Gives either all triples or only primitive ones.

http://www.mste.uiuc.edu/activity/triples/trip89code.html

Generates Pythagorean triples; also has TI program to do the same.

12.2 Sums of Two Squares

http://math.uh.edu/~minru/web/represent3.html

Applets to list integers that are expressible as the sum of two squares and to provide the squares in the sums

13.1 The Fibonacci Sequence

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibCalcX.html

Generates terms of the sequence, also the Lucas sequence.

http://smccd.net/accounts/kennedyc/cis284aa/FiboApp.htm

Generates terms of the sequence

Miscellaneous

http://www.flashpsychic.com/

Trick based on mod 9