 ## Discrete Math Calculators: (45) lessons

Affine Cipher
Builds the Affine Cipher Translation Algorithm from a string given an a and b value
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Automorphic Number
This calculator determines the nth automorphic number
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Boolean Algebra Multiplication
Determines the product of two expressions using boolean algebra.
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Chinese Remainder Theorem
Given a set of modulo equations in the form:
x ≡ a mod b
x ≡ c mod d
x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.
Given that the ni portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution
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Collatz Conjecture
Takes any natural number using the Collatz Conjecture and reduces it down to 1.
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Composite Number
This calculator determines the nth composite number. Helps you generate composite numbers.
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Congruence Modulo n
Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n).
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Cross Partitions
Given a set of partitions, this determines the cross partitions.
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Decagonal Number
This calculator determines the nth decagonal number
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Derangements - Subfactorials
Calculates the number of derangements/subfactorial !n.
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Digit Problems
Determines how many (n) digit numbers can be formed based on a variety of criteria.
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Diophantine Equations
Solves for ax + by = c using integer solutions if they exist
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Euclids Algorithm and Euclids Extended Algorithm
Given 2 numbers a and b, this calculates the following
1) The Greatest Common Divisor (GCD) using Euclids Algorithm
2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm Extended Euclidean Algorithm
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Eulers Totient (φ)
Given a positive integer (n), this calculates Euler's totient, also known as φ
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Fermats Little Theorem
For any integer a and a prime number p, this demonstrates Fermats Little Theorem.
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Finite Field
Demonstrates the addition table and multiplication table for a finite field (Galois Field) of n denoted GF(n).
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Gamma Constant γ
This calculator generates 5000 iterations for the development of the gamma constant γ
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Group Combinations
Given an original group of certain types of member, this determines how many groups/teams can be formed using a certain condition.
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Heptagonal Number
This calculator determines the nth heptagonal number
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Hexagonal Number
This calculator determines the nth hexagonal number
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Hyperbolic Function
Calculates hyperbolic function values: sinh, cosh, tanh, csch, sech, coth
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Hyperbolic Inverse
Calculates hyperbolic function values: arcsinh, arccosh, arctanh, arccsch, arcsech, arccoth
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Interpolation
Given a set of data, this interpolates using the following methods:
* Linear Interpolation
* Nearest Neighbor (Piecewise Constant)
* Polynomial Interpolation
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Interval Partition
Given a partitioned interval, this evaluates the norm (mesh) by calculating each subinterval
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Lagrange Four Square Theorem (Bachet Conjecture)
Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.
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Letter Arrangements in a Word
Given a word, this determines the number of unique arrangements of letters in the word.
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Linear Congruence
Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists
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Linear Congruential Generator
Using the linear congruential generator algorithm, this generates a list of random numbers based on your inputs
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Modular Exponentiation and Successive Squaring
Solves xn mod p using the following methods:
* Modular Exponentiation
* Successive Squaring
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Modulus
Given 2 integers a and b, this modulo calculator determines a mod b or simplifies modular arithmetic such as 7 mod 3 + 5 mod 8 - 32 mod 5
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Modus Ponens
Shows modus Ponens definition and examples
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Modus Tollens
Shows Modus Tollens definition and examples
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Multifactorials
Calculates the multifactorial n!(m)
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Nonagonal Number
This calculator determines the nth nonagonal number
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Number Property
This calculator determines if an integer you entered has any of the following properties:
* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)
* Evil Numbers or Odious Numbers
* Perfect Numbers, Abundant Numbers, or Deficient Numbers
* Triangular Numbers
* Prime Numbers or Composite Numbers
* Automorphic (Curious)
* Undulating Numbers
* Square Numbers
* Cube Numbers
* Palindrome Numbers
* Repunit Numbers
* Apocalyptic Power
* Pentagonal
* Tetrahedral (Pyramidal)
* Narcissistic (Plus Perfect)
* Catalan
* Repunit
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Octagonal Number
This calculator determines the nth octagonal number
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Ordered and Unordered Partitions
Given a population size (n) and a group population of (m), this calculator determines how many ordered or unordered groups of (m) can be formed from (n)
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Pentagonal Number
This calculator determines the nth pentagonal number
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Primitive Root
Given a prime number p and a potential root of b, this determines if b is a primitive root of p.
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Quotient-Remainder Theorem
Given 2 positive integers n and d, this displays the quotient remainder theorem.
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Rectangular Number
This calculator determines the nth rectangular number
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Sieve of Eratosthenes
Using the Sieve of Eratosthenes algorithm, this will show how many prime numbers are less than a number (n).
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Square Number
This calculator determines the nth square number
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Triangular Number
This calculator determines the nth triangular number. Generates composite numbers.
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Truth Tables
Sets up a truth table based on a logical statement of 1, 2 or 3 letters with statements such as propositions, equivalence, conjunction, disjunction, negation. Includes modus ponens.
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