Divisible

A number n is said to be divisible by d if d is a divisor of n, denoted d|n ("d divides n"). The converse of d|n is pn ("p does not divide n").

The function Divisible [n, d] returns True if an integer n is divisible by an integer d.

The product of any n consecutive integers is divisible by n!. The sum of any n consecutive integers is divisible by n if n is odd, and by n/2 if n is even.

See also

Divide, Divisibility Tests, Divisible Module, Divisor, Divisor Function

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References

Guy, R. K. "Divisibility." Ch. B in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 44-104, 1994.Jones, G. A. and Jones, J. M. "Divisibility." Ch. 1 in Elementary Number Theory. Berlin: Springer-Verlag, pp. 1-17, 1998.Nagell, T. "Divisibility." Ch. 1 in Introduction to Number Theory. New York: Wiley, pp. 11-46, 1951.

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Divisible

Cite this as:

Weisstein, Eric W. "Divisible." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Divisible.html

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