Discussion

If n=1+x, where x is a product of four consecutive positive integers, then which of the following is true?

A. n is odd

B. n is prime

C. n is a perfect square

Answer: A

Since xx is the product of four consecutive integers, it is always divisible by 4, i,.e., it is always even. So, 1+x is always odd.

n=1+x

x=(y−1)(y)(y+1)(y+2)=y(y2−1)(y+2)=(y3−y)(y+2)=y4+2y3−y2−2y

⇒1+x=y4+2y3−y2−2y+1=y4+y2+1+2y3−2y2−2y=(y2+y−1)2

So, 1+x is a perfect square as we can see. Hence, option A is the correct choice.

No comment is present. Be the first to comment.

Loading…