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Question: discrete mathematics determine whether the statement is true or false...

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discrete mathematics

Determine whether the statement is true or false. Any product of four consecutive integers is one less than a perfect square. Justify your answer with a proof or a counterexample, as appropriate. Use only the definitions of the terms and laws of algebra to justify the statements in your proof.

Note: Two integers are consecutive if, and only if, one is one more than the other. š‘Ž, š‘ š‘š‘œš‘›š‘ š‘’š‘š‘¢š‘”š‘–š‘£š‘’ ā†” (š‘Ž + 1 = š‘) āˆØ (š‘ + 1 = š‘Ž) Note: An integer š‘Ž is a perfect square if and only if it equals the square of an integer. š‘Ž āˆˆ š‘ š‘–š‘  š‘Ž š‘š‘’š‘Ÿš‘“š‘’š‘š‘” š‘ š‘žš‘¢š‘Žš‘Ÿš‘’ ā†” āˆƒš‘ āˆˆ š‘ | š‘Ž = š‘^2

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