To divide is to perform the operation of division, i.e., to see how many times a divisor d goes into another number n. n divided by d is written or . The result need not be an integer, but if it is, some additional terminology is used. is read "d divides n" and means that d is a divisor of n. In this case, n is said to be divisible by d. Clearly, and . By convention, for every n except 0 (Hardy and Wright 1979, p. 1). The "divisibility" relation satisfies

where the symbol means implies.

is read " does not divide n" and means that is not a divisor of n. means divides b exactly. If n and d are relatively prime, the notation or sometimes is used.

 

Congruence, Divides, Divisible, Divisibility Tests, Division, Divisor, Greatest Dividing Exponent, k-ary Divisor, Relatively Prime