Number Theory

Number

• Real Number

  • Rational Number (-1, -0.5, 0, +0.5, +1)

    • Integer Number (-1, 0, +1)

    • Whole (0, 1, 2, 3)

    • Natural/Counting Number (1, 2, 3, 4)

  • Irrational Number (sqrt(2), pi)

• Imaginary Number ( a+ib )

Number Theory Topic

• Divisibility

• Modulus

• Find Divisor/Factor

• Number of Divisors

• Sum of Divisors

• Perfect/Abundant/Deficient Number

• GCD, LCM (Normal, Euclidean Algorithm, Extended Euclidean Algorithm, Euler Phi, Inverse Phi)

• Co-Prime

• Euler’s Totient Function

• Prime (Normal, Sieve, Bitwise Sieve, Segmented Sieve)

• Prime Factorization

  • Number of Divisors

  • Sum of Divisors

• Different Number and Series

• Big Integer

• Modular Arithmetic (Addition, Subtraction, Multiplication)

• Modular Inverse (Fermat’s Theorem)

• Exponentiation

• Big Mod (a^b%m)

• Factorial

• Combinatorics

  • Counting

  • Combination

  • Permutation

• Probability

• Expectation

UVa Problem

1. 382 - Perfection

2. 371 - Ackermann Functions

3. 406 - Prime Cuts

4. 10924 - Prime Words

5. 10235 - Simply Emirp