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  2. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2][3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4.

  3. Division (mathematics) - Wikipedia

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

    Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations ...

  4. 1001 (number) - Wikipedia

    en.wikipedia.org/wiki/1001_(number)

    Two properties of 1001 are the basis of a divisibility test for 7, 11 and 13. The method is along the same lines as the divisibility rule for 11 using the property 10 ≡ -1 (mod 11). The two properties of 1001 are 1001 = 7 × 11 × 13 in prime factors 10 3 ≡ -1 (mod 1001) The method simultaneously tests for divisibility by any of the factors ...

  5. Divisibility sequence - Wikipedia

    en.wikipedia.org/wiki/Divisibility_sequence

    Divisibility sequence. In mathematics, a divisibility sequence is an integer sequence indexed by positive integers n such that. for all m, n. That is, whenever one index is a multiple of another one, then the corresponding term also is a multiple of the other term. The concept can be generalized to sequences with values in any ring where the ...

  6. Division algorithm - Wikipedia

    en.wikipedia.org/wiki/Division_algorithm

    Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.

  7. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    A bijection with the sums to n is to replace 1 with 0 and 2 with 11. The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2 F n . For example, out of the 16 binary strings of length 4, there are 2 F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110.

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