KVPY SA Exam 2011 Question Paper

Question : 10 of 80

Marks: +1, -0

The number o f distinct prime divisors of the number

5 12^3-253^3 -259^3

Solution:

(512)^3 - 253^3 - 259^3

= (512)^3 - [(253^3 ) + (259)^3 ]

= (512)^3 - (253 + 259)

(253^2 + 259^2 - (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)]

= 2^9 . 3 . (253) (259)

= 2^9 . 3 (11) (23) (7) (37)

6 prime divisors.

Go to Question:

Prev Question

Next Question