Prove the following theorem by direct proof method: ‘‘The square of an even integer is an even integer.’’

To prove the theorem "The square of an even integer is an even integer" using a direct proof, we start by recalling the definition of an even integer.

An integer \( n \) is defined as even if it can be expressed in the form \( n = 2k \), where \( k \) is an integer.

Proof:

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