I am having trouble with the following problem: Find the last three digits of 7^732. I know that I need to find the least residue of 7^732(mod 1000), so I calculate Phi(1000)=Phi(2^3)*Phi(5^3)=4*100=400, which means that 7^400==1(mod 1000)==1+7^332(mod 1000). And that's where I get stuck. I cannot seem to find a way to reduce this problem. Help! Thanks.