What are the ones, tens, and hundreds digits of 7^(2010)?
B bearej50 New member Joined Feb 16, 2009 Messages 21 Mar 23, 2010 #1 What are the ones, tens, and hundreds digits of 7^(2010)?
D daon Senior Member Joined Jan 27, 2006 Messages 1,284 Mar 24, 2010 #2 Use mod 10 to find the ones digit Use mod 100 to find the 10s digit, subtract previous etc Use the fact that 7^(Phi(10))=7^4=1 mod 10.
Use mod 10 to find the ones digit Use mod 100 to find the 10s digit, subtract previous etc Use the fact that 7^(Phi(10))=7^4=1 mod 10.
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Mar 24, 2010 #3 This should help: . . . \(\displaystyle 7^{20}\:\equiv\:001 \text{( mod 1000)}\)
