dave13 wrote:

thank you

Bunuel one question

why do you assume that least value is 8 ?

whats your reasoning ? can you please explain

as \(n\) is an integer, the least value of \(n\) is obtained when \(k=8\) -And how did you figure out these values

\(8\) for \(k=2^3*2^4\), \(12\) for \(k=2^3*3^4\)

for instance this \(k=2^3*2^4\), how should I understand it ? for example for n to be 4 k= 8 but you didn't break down this into exponents unlike other examples

hey

pushpitkc, may be you can explain/answer the above questions

thanks!

Hey

dave13Let me try and explain this question once again.

If \(n^4\) is divisible by 32, we have been asked to find a remainder(from answer options) when n is divided by 32.

First, we have to prime-factorize 32 which is \(2^5\).

Now, n has to contain a minimum of \(2^2\) in order for \(n^4\) to be divisible by \(32(2^5)\). In order to validate our answer,

we can test a smaller value - If n had only one 2, then \(n^4\) would contain \(2^4\) and that would not be divisible by 32.

Hope this clears your confusion!

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