Consider the following statements in respect of p=n(n+1)(n+2)(n+3)+1, where n is a natural number:<br>I. p is <strong>ALWAYS</strong> odd<br>II. p is a perfect square<br>Which of the statements given above is/are correct?
- A. I only
- B. II only
- C. Both I and II ✓
- D. Neither I nor II
Correct Answer: C. Both I and II
Explanation
For I: Product of 4 consecutive integers n(n+1)(n+2)(n+3) is even, so p = \text{even} + 1 is always odd (True). For II: Let k = n^2+3n. Then p = k(k+2)+1 = (k+1)^2 = (n^2+3n+1)^2, which is a perfect square (True).
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