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The number of distinct prime divisors of the number ` 512^(3) - 253^(3) - 259^(3)` isA. 4B. 5C. 6D. 7 |
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Answer» Correct Answer - C `(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. |
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