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If P = n(n² - 12)(n² - 22)(n² - 32)...(n² - r²), n > r, n N, then P is divisible by

1. (2r + 2)!

2. (2r - 1)!

3.(2r + 1)!

4.(2r - 2)!

6 Answers

see it is the product of 2r+1 consecutive numbers...

hence it is divisible by (2r+1)!

also, because it is divisible by (2r+1)! so it has to be divisible by the smaller factorials

hence the answer should be 2, 3, 4

Nishant sir, how are these numbers consecutive.
i think the question should be P=n(n-1)(n-2)...(n-r²)

@Nishant Sir : I got the logic Thanks:)

@figonacci
P=n(n-1²)(n-2²)...(n-r²)

= (n-r)(n-r+1)..........n(n+1)(n+2)......(n+r)

oh i didnt guess 12 was 1² :)

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