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The number of integer value(s) of n when...

The number of integer value(s) of n when `3^512`-1 is divided by `2^n` is/are

Text Solution

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`3^512 - 1 = (3^256)^2 - 1`
`= (3^256 - 1)(3^256 + 1)`
`= ((3^128)^2 - 1^2)(3^256 + 1)`
`= (3^128 -1)(3^128 +1)(3^256 +1)`
`3^512 - 1 = (3^64 - 1)(3^64 + 1)(3^128 + 1)(3^256+1)`
`= (3^32 - 1)(3^32+1)`
`= (3^16 - 1)(3^16+1)`
`= (3^8 - 1)(3^8+1)`
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