represents the domain of integers, as in x∈Integers.
Integers
represents the domain of integers, as in x∈Integers.
Details
- x∈Integers evaluates immediately if x is a numeric quantity.
- Simplify [expr∈Integers,assum] can be used to try to determine whether an expression is an integer under the given assumptions.
- (x1|x2|…)∈Integers and {x1,x2,…}∈Integers test whether all xi are integers.
- IntegerQ [expr] tests only whether expr is manifestly an integer (i.e. has head Integer ).
- Integers is output in StandardForm or TraditionalForm as TemplateBox[{}, Integers]. This typeset form can be input using ints.
Examples
open all close allBasic Examples (3)
Seven is an integer:
If is an integer, so is :
Find positive integer solutions of a Pell equation:
Scope (7)
Test domain membership of a numeric expression:
Make domain membership assumptions:
Specify the default domain over which a function should work:
Find integer roots of a high-degree polynomial:
Find a representation of an integer as a sum of seven squares:
Solve an optimization problem over the integers:
Test whether several numbers are integers:
If any number is explicitly non-integer, the result is False :
TraditionalForm formatting:
Related Guides
History
Introduced in 1999 (4.0) | Updated in 2017 (11.2)
Text
Wolfram Research (1999), Integers, Wolfram Language function, https://reference.wolfram.com/language/ref/Integers.html (updated 2017).
CMS
Wolfram Language. 1999. "Integers." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Integers.html.
APA
Wolfram Language. (1999). Integers. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Integers.html
BibTeX
@misc{reference.wolfram_2025_integers, author="Wolfram Research", title="{Integers}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Integers.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_integers, organization={Wolfram Research}, title={Integers}, year={2017}, url={https://reference.wolfram.com/language/ref/Integers.html}, note=[Accessed: 04-January-2026]}