Polynomials

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Factorials

    1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?
    1. 30 < P < 40
    2. 10 < P < 20
    3. 30 < P < 40
    4. P > 40

 

  • Correct Answer
    Choice D. P > 40

Explanatory Answer

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Detailed Solution

1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!)
= 51! – 1 (per the logic we have seen earlier)
51! is a multiple of all prime numbers from 2 upto (and including) 47.
So, 51! – 1 should not be a multiple of any prime from 0 to 50. So, the smallest prime that divides 51! – 1 should be more than 50.
Answer choice (d)


Correct Answer: P > 40.



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