\(2^4\equiv1\left(mod5\right)\\ \Rightarrow\left(2^4\right)^{25}\equiv1^{25}=1\left(mod5\right)\\ \Rightarrow2^{100}\equiv1\left(mod5\right)\\ \Rightarrow2^{100}-1\equiv0\left(mod5\right)\\ \Rightarrow\left(2^{100}-1\right)⋮5\\ \text{Mà }2^{100}-1>5\)
Vậy \(2^{100}-1\) là hợp số