Haryana Police Constable Model Paper 8

Question : 15 of 100

Marks: +1, -0

2^{18} −1

is divisible by:

Solution:

Formula used:

\a^{2} - \b^{2} = (\a + \b)(\a - \b)

\a^{3} -\b^{3} = (\a - \b)(\a^{2} + \b^{2} + \ab)

Calculation:

⇒ (2^{9} - 1)(2^{9} + 1)

⇒ [(2^{3})^{3} - 1)(2^{9} + 1)]

⇒ [(2^{3} - 1)(2^{6} + 1 + 2^{3})(2^{9} + 1)]

⇒ [(8- 1)(64 + 1 + 8)(2^{9} + 1)]

⇒ [(7) × (73) × (2^{9} + 1)]

Since, 7 is one of the factor of

21^{8} - 1

∴ It will be divisible by 7.

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