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IntegerQ
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IntegerQ

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IntegerQ[expr]

gives True if expr is an integer, and False otherwise.

Details

  • IntegerQ[expr] returns False unless expr is manifestly an integer (i.e. has head Integer).
  • Simplify[expr∈Integers] can be used to try to determine whether an expression is mathematically equal to an integer.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

IntegerQ tests whether an expression is explicitly an integer:

In[1]:=1
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https://wolfram.com/xid/0wgls4z-6xlso
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0wgls4z-c6ay2v
Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Test whether an array consists of all integers:

In[1]:=1
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https://wolfram.com/xid/0wgls4z-e2n24
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0wgls4z-57cin
Out[2]=2

Make a test for Gaussian integers:

In[1]:=1
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https://wolfram.com/xid/0wgls4z-c4775q
In[2]:=2
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https://wolfram.com/xid/0wgls4z-bq1v0i
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

Integers have head Integer:

In[1]:=1
✖
https://wolfram.com/xid/0wgls4z-cn335t
In[2]:=2
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https://wolfram.com/xid/0wgls4z-ddw65m
Out[2]=2

An expression may have head Integer, but IntegerQ gives False:

In[1]:=1
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https://wolfram.com/xid/0wgls4z-damflh
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0wgls4z-ihtg4z
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

Expressions that do not evaluate to integers explicitly will still give False:

In[1]:=1
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https://wolfram.com/xid/0wgls4z-fqsmkl
In[2]:=2
✖
https://wolfram.com/xid/0wgls4z-d6xt37
Out[2]=2

It is necessary to use symbolic simplification first:

In[3]:=3
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https://wolfram.com/xid/0wgls4z-3i2q6
Out[3]=3
Wolfram Research (1988), IntegerQ, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerQ.html (updated 1999).
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Wolfram Research (1988), IntegerQ, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerQ.html (updated 1999).

Text

Wolfram Research (1988), IntegerQ, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerQ.html (updated 1999).

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Wolfram Research (1988), IntegerQ, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerQ.html (updated 1999).

CMS

Wolfram Language. 1988. "IntegerQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1999. https://reference.wolfram.com/language/ref/IntegerQ.html.

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Wolfram Language. 1988. "IntegerQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1999. https://reference.wolfram.com/language/ref/IntegerQ.html.

APA

Wolfram Language. (1988). IntegerQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IntegerQ.html

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Wolfram Language. (1988). IntegerQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IntegerQ.html

BibTeX

@misc{reference.wolfram_2025_integerq, author="Wolfram Research", title="{IntegerQ}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/IntegerQ.html}", note=[Accessed: 09-July-2025 ]}

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@misc{reference.wolfram_2025_integerq, author="Wolfram Research", title="{IntegerQ}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/IntegerQ.html}", note=[Accessed: 09-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_integerq, organization={Wolfram Research}, title={IntegerQ}, year={1999}, url={https://reference.wolfram.com/language/ref/IntegerQ.html}, note=[Accessed: 09-July-2025 ]}

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@online{reference.wolfram_2025_integerq, organization={Wolfram Research}, title={IntegerQ}, year={1999}, url={https://reference.wolfram.com/language/ref/IntegerQ.html}, note=[Accessed: 09-July-2025 ]}