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 [n, d] returns 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.

Referenced on Wolfram|Alpha

Divisible

Cite this as:

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

Subject classifications