99's

Since $\lambda(99)=30$ , we have $2^{99}=2^{3\times 30+9}\equiv 2^9=512\equiv \boxed{17} \pmod{99}$

click here for full solution . There is other solution also: Enter the following coding in java: double x= ((Math.pow(2, 99))%99); System.out.println(x);