Fractional part of the number \[\frac{4^{2022}}{15}\] is equal to
Solutions · 1
Official solution
\[4^{2022}=2^{4044}=(2^4)^{1011}=16^{1011}=(1+15)^{1011}\]
Expanding, all terms except the constant 1 are divisible by 15.
\[\left\{\frac{4^{2022}}{15}\right\}=\frac{1}{15}\]