It is given that 5 does <strong>NOT</strong> divide n-1, n and n+1, where n is a positive integer. Which one of the following is correct?

Explanation

Any positive integer n can be expressed as 5k, 5k+1, 5k+2, 5k+3, 5k+4. Since n, n-1, n+1 are not divisible by 5, n must be of the form 5k+2 or 5k+3. In both cases, n^2 \equiv 4 \equiv -1 \pmod 5. Therefore, n^2+1 is perfectly divisible by 5.

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