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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. Greatest common divisor - Wikipedia

   en.wikipedia.org/wiki/Greatest_common_divisor

   Appearance. In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is ...

5. Euclid's lemma - Wikipedia

   en.wikipedia.org/wiki/Euclid's_lemma

   Euclid's lemma. In algebra and number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers: [note 1] Euclid's lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a or b. For example, if p = 19, a = 133, b = 143, then ab = 133 × 143 = 19019 ...

6. Fibonacci sequence - Wikipedia

   en.wikipedia.org/wiki/Fibonacci_sequence

   In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from ...

7. Zsigmondy's theorem - Wikipedia

   en.wikipedia.org/wiki/Zsigmondy's_theorem

   In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if are coprime integers, then for any integer , there is a prime number p (called a primitive prime divisor) that divides and does not divide for any positive integer , with the following exceptions: This generalizes Bang's theorem, [1] which states that if and is ...