Successive powers of 443 end in 443; 249; 307; 001. These then repeat (see below).
The first of these occurs when mod(power,4) = 1, the second when mod(power,4) = 2, the third when mod(power,4) = 3 and the fourth when mod(power,4) = 0.
Since mod(443,4) = 3, the last three digits of 443443 are 307.
Successive powers of 443 end in 443; 249; 307; 001. These then repeat (see below).
The first of these occurs when mod(power,4) = 1, the second when mod(power,4) = 2, the third when mod(power,4) = 3 and the fourth when mod(power,4) = 0.
Since mod(443,4) = 3, the last three digits of 443443 are 307.