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

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