Q

# This is a doubt from Binomial theorem and its simple applications

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$\left\{\frac{2^{408}}{15}\right\}=\frac{k}{15}.\:Then\:k\:is\:$

$\\\left\{\frac{2^{403}}{15}\right\}=\frac{k}{15}\\2^{403}=8\cdot2^{400}=8\cdot 16^{100}\\\Rightarrow 8\left(1+15\right)^{100}=8(1+15\lambda)\\(Apply\:binomial\:expension)\\reminder\:\:is\:\:8\\k=8$