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  2. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    If the number of digits is even, add the first and subtract the last digit from the rest. The result must be divisible by 11. 918,082: the number of digits is even (6) → 1808 + 9 − 2 = 1815: 81 + 1 − 5 = 77 = 7 × 11. If the number of digits is odd, subtract the first and last digit from the rest. The result must be divisible by 11.

  3. Parity (mathematics) - Wikipedia

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

    Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That ...

  4. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    If one considers only the odd numbers in the sequence generated by the Collatz process, then each odd number is on average ⁠ 3 / 4 ⁠ of the previous one. [16] (More precisely, the geometric mean of the ratios of outcomes is ⁠ 3 / 4 ⁠.) This yields a heuristic argument that every Hailstone sequence should decrease in the long run ...

  5. Parity bit - Wikipedia

    en.wikipedia.org/wiki/Parity_bit

    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. If the count of bits with a value of 1 is odd, the count is already odd so the parity bit's value is 0.

  6. Parity function - Wikipedia

    en.wikipedia.org/wiki/Parity_function

    Parity only depends on the number of ones and is therefore a symmetric Boolean function.. The n-variable parity function and its negation are the only Boolean functions for which all disjunctive normal forms have the maximal number of 2 n − 1 monomials of length n and all conjunctive normal forms have the maximal number of 2 n − 1 clauses of length n.

  7. Exclusive or - Wikipedia

    en.wikipedia.org/wiki/Exclusive_or

    With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd. [1] It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR excludes that case. Some informal ways of describing XOR are ...

  8. Goldbach's weak conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_weak_conjecture

    For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3). In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. [ 2 ]

  9. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    The ordinary factorial, when extended to the gamma function, has a pole at each negative integer, preventing the factorial from being defined at these numbers. However, the double factorial of odd numbers may be extended to any negative odd integer argument by inverting its recurrence relation!! = ()!! to give !! = (+)!! +.