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log(m)N = alpha + beta where alpha in 1,...

`log_(m)N = alpha + beta` where `alpha in 1, beta in [0, 1]`
If `m` and `alpha` are reletively prime and `alpha + n = 7` then which of the following is not the minimum value of `N`

A

`64`

B

`63`

C

`125`

D

`124`

Text Solution

Verified by Experts

The correct Answer is:
A, B
If `alpha = 2m m = 65`, If `alpha = 5, m = 5`
`log_(epsilon)N = (2 + beta), log_(2)N = 5 + beta`
`N in [5^(2), 5^(3)) = [25, 125), N in [2^(5), 2^(6)) = [32, 64)`
`:. N_(min) = 124, :. N_(max) = 63`
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