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Prove that (n !+1) is not divisible by a...

Prove that `(n !+1)` is not divisible by any natural number between `2a n dndot`

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Let p be divisible by k and r be any natural number between 1 and k. If p+r is divided by k, we obtian r as the remainder.
Now, `n!=1xx2xx3xx4xx..xx(n-1)n`
Therefore, n! is divisible by every natural number between 2 and n. So, n!+1, when divided by any natural number between 2 and n, leaves 1 as the remainder. Hence, n!+1 is not divisible by any natural number between 2 and n.
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