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Discrete Mathematics Help. Prove the given statement. If n is an even integer, then n² - 1 is odd.

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I posted the question on Chegg but I believe the answer was incorrect. In the person s solution, when providing information for the proof, they started by saying "x is an odd integer" and "x - 1 and x + 1 are even integers" which is obviously incorrect, because my problem states "x is an even integer" which would also mean "x+1 and x-1" would be odd integers. Anyways, how would one prove the validity of this statement?

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Even integers can be expressed as 2k, where k is any integer Odd integers can be expressed as 2k+1, where k is any integer n is an even integer ----> n = 2k n² + 1 = (2k)² + 1 = 4k² + 1 = 2(2k²) + 1 ----> odd

            
        

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