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IntegerQ[expr]

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

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IntegerQ

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

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Basic Examples  (1)

IntegerQ tests whether an expression is explicitly an integer:

Wolfram Language code: IntegerQ[4]
Wolfram Language code: IntegerQ[4 + x]

Applications  (2)

Test whether an array consists of all integers:

Wolfram Language code: ArrayQ[{{1, 4}, {9, 16}}, _, IntegerQ]
Wolfram Language code: ArrayQ[{{1., 4.}, {9., 16.}}, _, IntegerQ]

Make a test for Gaussian integers:

Wolfram Language code: gaussIntegerQ[x_] := IntegerQ[Re[x]] && IntegerQ[Im[x]]
Wolfram Language code: gaussIntegerQ[1 + 2 I]

Properties & Relations  (2)

Integers have head Integer:

Wolfram Language code: x = 8529050985092184098210948213048204809218402184;
Wolfram Language code: {IntegerQ[x], Head[x]}

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

Wolfram Language code: IntegerQ[Integer[x]]
Wolfram Language code: IntegerQ[Integer[1.2]]

Possible Issues  (1)

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

Wolfram Language code: x = GoldenRatio - 1 / GoldenRatio;
Wolfram Language code: IntegerQ[x]

It is necessary to use symbolic simplification first:

Wolfram Language code: FullSimplify[x]
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).

CMS

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

BibTeX

@misc{reference.wolfram_2026_integerq, author="Wolfram Research", title="{IntegerQ}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/IntegerQ.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_integerq, organization={Wolfram Research}, title={IntegerQ}, year={1999}, url={https://reference.wolfram.com/language/ref/IntegerQ.html}, note=[Accessed: 12-June-2026]}