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Mathematica® Teacher's Edition (2002)

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IntegerQ

FilledSmallSquare IntegerQ[expr] gives True if expr is an integer, and False otherwise.

FilledSmallSquare IntegerQ[expr] returns False unless expr is manifestly an integer (i.e., has head Integer).
FilledSmallSquare Simplify[expr Integers] can be used to try to determine whether an expression is mathematically equal to an integer.
FilledSmallSquare See The Mathematica Book on the web: Section 2.3.5 and Section 3.1.1.
FilledSmallSquare See also: EvenQ, OddQ, NumberQ, TrueQ, Element.