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  2. 68 (number) - Wikipedia

    en.wikipedia.org/wiki/68_(number)

    68 is a composite number; a square-prime, of the form (p 2, q) where q is a higher prime. It is the eighth of this form and the sixth of the form (2 2.q). 68 is a Perrin number. [1] It has an aliquot sum of 58 within an aliquot sequence of two composite numbers (68, 58,32,31,1,0) to the Prime in the 31-aliquot tree.

  3. 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 ...

  4. Eventually (mathematics) - Wikipedia

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

    The square of a prime is eventually congruent to 1 mod 24 (specifically, this is true for all primes greater than 3). The factorial of a natural number eventually ends in the digit 0 (specifically, this is true for all natural numbers greater than 4).

  5. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal to zero. Thus a non-negative number is either zero or positive. Non-positive numbers: Real numbers that are less ...

  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. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    In 1975, Hugh Lowell Montgomery and Bob Vaughan showed that "most" even numbers are expressible as the sum of two primes. More precisely, they showed that there exist positive constants c and C such that for all sufficiently large numbers N, every even number less than N is the sum of two primes, with at most CN 1 − c exceptions.

  8. Parity of zero - Wikipedia

    en.wikipedia.org/wiki/Parity_of_zero

    In this sense, 0 is the "most even" number of all. [1] Among the general public, the parity of zero can be a source of confusion. In reaction time experiments, most people are slower to identify 0 as even than 2, 4, 6, or 8. Some teachers—and some children in mathematics classes—think that zero is odd, or both even and odd, or neither.

  9. Proof of Fermat's Last Theorem for specific exponents

    en.wikipedia.org/wiki/Proof_of_Fermat's_Last...

    The multiplication of two odd numbers is always odd, but the multiplication of an even number with any number is always even. An odd number raised to a power is always odd and an even number raised to power is always even, so for example x n has the same parity as x. Consider any primitive solution (x, y, z) to the equation x n + y n = z n.

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