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KVPY2011MathematicsBinomial Theorem

The number of distinct prime divisors of the number 512³-253³-259³ is

Options

  1. A4
  2. B5
  3. C6
  4. D7

Correct answer

C. 6

Step-by-step solution

array l (512)³-253³-259³ =(512)³- [ (253³ )+(259)³ ] =(512)³-(253+259) (253²+259²-(253)(259) . =(512)³-(512) [(253+259)²-2(253)(259)-(253)(259) ] =512 [(512)²- (512)²-3(253)(259) ] =(512)[3(253)(259)] =2⁹ .3 .(253)(259) =2⁹ .3(11)(23)(7)(37) array 6 prime divisors.

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