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  2. Parity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Parity_(mathematics)

    The even numbers form an ideal in the ring of integers, [13] but the odd numbers do not—this is clear from the fact that the identity element for addition, zero, is an element of the even numbers only. An integer is even if it is congruent to 0 modulo this ideal, in other words if it is congruent to 0 modulo 2, and odd if it is congruent to 1 ...

  3. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For any integer n, n ≡ 1 (mod 2) if and only if ⁠ 3n + 1 / 2 ⁠ ≡ 2 (mod 3). Equivalently, ⁠ 2n − 1 / 3 ⁠ ≡ 1 (mod 2) if and only if n ≡ 2 (mod 3). Conjecturally, this inverse relation forms a tree except for a 1–2 loop (the inverse of the 1–2 loop of the function f(n) revised as indicated above).

  4. Odd–even sort - Wikipedia

    en.wikipedia.org/wiki/Odd–even_sort

    It functions by comparing all odd/even indexed pairs of adjacent elements in the list and, if a pair is in the wrong order (the first is larger than the second) the elements are switched. The next step repeats this for even/odd indexed pairs (of adjacent elements). Then it alternates between odd/even and even/odd steps until the list is sorted.

  5. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    Thus if n is a large even integer and m is a number between 3 and ⁠ n / 2 ⁠, then one might expect the probability of m and n − m simultaneously being prime to be ⁠ 1 / ln m ln(n − m) ⁠. If one pursues this heuristic, one might expect the total number of ways to write a large even integer n as the sum of two odd primes to be roughly

  6. Singly and doubly even - Wikipedia

    en.wikipedia.org/wiki/Singly_and_doubly_even

    A doubly even number is an integer that is divisible more than once by 2; it is even and its quotient by 2 is also even. The separate consideration of oddly and evenly even numbers is useful in many parts of mathematics, especially in number theory, combinatorics , coding theory (see even codes ), among others.

  7. Thue–Morse sequence - Wikipedia

    en.wikipedia.org/wiki/Thue–Morse_sequence

    If the number of ones in this binary expansion is odd then t n = 1, if even then t n = 0. [2] That is, t n is the even parity bit for n. John H. Conway et al. deemed numbers n satisfying t n = 1 to be odious (intended to be similar to odd) numbers, and numbers for which t n = 0 to be evil (similar to even) numbers.

  8. Parity bit - Wikipedia

    en.wikipedia.org/wiki/Parity_bit

    If the count of 1s in a given set of bits is already even, the parity bit's value is 0. In the case of odd parity, the coding is reversed. For a given set of bits, if the count of bits with a value of 1 is even, the parity bit value is set to 1 making the total count of 1s in the whole set (including the parity bit) an odd number.

  9. Even code - Wikipedia

    en.wikipedia.org/wiki/Even_code

    A binary code is called an even code if the Hamming weight of each of its codewords is even. An even code should have a generator polynomial that include (1+x) minimal polynomial as a product. Furthermore, a binary code is called doubly even if the Hamming weight of all its codewords is divisible by 4. An even code which is not doubly even is ...