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    Prime number proof

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    Prove that if p is a prime number, then p divides

    , for all n≥p.

    Here [r] denotes the greatest integer ≤ r , for any real number r.

    Does this result generalize to a result about instead of p ?

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    Solution Preview

    Please see the attachment.

    For any prime , we have . So we can assume . Now for any continuous integers , we also have

    Let's come back to the problem. ...

    Solution Summary

    This solution shows a prime number proof. The results generalized to a result are analyzed.