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  2. Table of divisors - Wikipedia

    en.wikipedia.org/wiki/Table_of_divisors

    a prime number has only 1 and itself as divisors; that is, d(n) = 2 a composite number has more than just 1 and itself as divisors; that is, d ( n ) > 2 a highly composite number has a number of positive divisors that is greater than any lesser number; that is, d ( n ) > d ( m ) for every positive integer m < n .

  3. Integer partition - Wikipedia

    en.wikipedia.org/wiki/Integer_partition

    3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1. The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. An individual summand in a partition is called a part.

  4. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful. The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd. The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd.

  5. Division (mathematics) - Wikipedia

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

    However, this number of times or the number contained (divisor) need not be integers. The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that ...

  6. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    Starting with other integers. Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P ...

  7. Fermat's theorem on sums of two squares - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem_on_sums_of...

    For the avoidance of ambiguity, zero will always be a valid possible constituent of "sums of two squares", so for example every square of an integer is trivially expressible as the sum of two squares by setting one of them to be zero. 1. The product of two numbers, each of which is a sum of two squares, is itself a sum of two squares.

  8. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to the left. This process is repeated until all digits have been added. [ 65 ] Other methods used for integer additions are the number line method, the partial sum method, and the compensation method. [ 66 ]

  9. Composite number - Wikipedia

    en.wikipedia.org/wiki/Composite_number

    [1] [2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. [3] [4] E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself.

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