# Integers

represents the domain of integers, as in xIntegers.

# Details • xIntegers evaluates immediately if x is a numeric quantity.
• Simplify[exprIntegers,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 . This typeset form can be input using ints .

# Examples

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## Basic 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: