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  2. Parity (mathematics) - Wikipedia

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

    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 is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any even number is 0, 2, 4, 6, or 8.

  3. Even and odd ordinals - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_ordinals

    Every limit ordinal (including 0) is even. The successor of an even ordinal is odd, and vice versa. [1] [2] Let α = λ + n, where λ is a limit ordinal and n is a natural number. The parity of α is the parity of n. [3] Let n be the finite term of the Cantor normal form of α. The parity of α is the parity of n. [4]

  4. Odds and evens (hand game) - Wikipedia

    en.wikipedia.org/wiki/Odds_and_evens_(hand_game)

    Even-Odd as an early form of roulette. This game was known by the Greeks (as artiazein) and Romans (as ludere par impar).In the 1858 Krünitzlexikon it says: [3] "The game Odds and Evens was very common amongst the Romans and was played either with tali, tesseris, or money and known as "Alea maior", or with nuts, beans and almonds and known as "Alea minor"."

  5. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    The number is taken to be 'odd' or 'even' according to whether its numerator is odd or even. Then the formula for the map is exactly the same as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd' such rational is multiplied by 3 and then 1 is added.

  6. Even and odd functions - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_functions

    They are named for the parity of the powers of the power functions which satisfy each condition: the function () = is even if n is an even integer, and it is odd if n is an odd integer. Even functions are those real functions whose graph is self-symmetric with respect to the y -axis, and odd functions are those whose graph is self-symmetric ...

  7. Perfect number - Wikipedia

    en.wikipedia.org/wiki/Perfect_number

    For example, the digital root of 8128 is 1, because 8 + 1 + 2 + 8 = 19, 1 + 9 = 10, and 1 + 0 = 1. This works with all perfect numbers 2 p − 1 ( 2 p − 1 ) {\displaystyle 2^{p-1}(2^{p}-1)} with odd prime p and, in fact, with all numbers of the form 2 m − 1 ( 2 m − 1 ) {\displaystyle 2^{m-1}(2^{m}-1)} for odd integer (not necessarily ...

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