Posted by Anonymous on Friday, August 3, 2012 at 10:01pm.
What are the final two digits of 7^177

math  Count Iblis, Friday, August 3, 2012 at 11:35pm
Phi(100) = 40, so the order of 7 (i.e. the smallest power to which you have to raise 7 to get 1) is a divisor of 40, and you easily find that it is 4.
Computing Mod 100 in the following:
7^4 = 2401 = 1
176 is a multiple of 4, so we have:
7^177 = 7

math  Reiny, Friday, August 3, 2012 at 11:37pm
Hint: take a look at the last two digits for the first few powers of 7
7^1 = 7 or 07
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = ......49
7^7 = ......43
7^8 = ......01
7^9 = ......07
7^10 = .... 49
I am sure you can do something with this pattern.
Answer This Question
Related Questions
 al gebr word problem MATH  parts to fix your car cost $55.35. the mechanic ...
 math  1. a door code is made up of six unique digits the last digit is 8. 2....
 math  Solve the mathematical puzzle. Determine the digits of F from these clues...
 MATH  What is my number if the hundreds digit is less than the tens digit and ...
 math (5th grade)  There are two 1's, two 2's, and two 3's. There is one digit ...
 math  A locker combination has three nonzero digits, and digits cannot be ...
 math  A locker combination has three nonzero digits, and digits cannot be ...
 Math  A locker combination has three nonzero digits, and digits cannot be ...
 math  What are the final two digits of 7124? Show work to support your answer
 Math  A locker combination has three nonzero digits, and digits cannot be ...
More Related Questions