If n = 1 + x where x is the product of four consecutive positive integers, then which of the following is/are true? A. n is odd B. n is prime C. n is a perfect square
Explanation:
Use the method of simulation, viz. take any sample values of x and verify that n is both odd as well as a perfect square.
Alternate solution: Let x = (n – 1) n (n + 1) (n + 2) = (n2 – 1) n(n + 2) = n4 + 2n3 – n2 – 2n
p = x + 1 = n4 + 2n3 – n2 – 2n + 1 = (n2 – n + 1)2
Hence, option (a).
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