SOLUTION: 4. Find the unit digit of 3^100. (The unit digit is the \ones digit".) Hint: Use Euler's Theorem or Fermat's Little Theorem with p = 5, and remember that 3^100 will be an odd num

Algebra ->  Rational-functions -> SOLUTION: 4. Find the unit digit of 3^100. (The unit digit is the \ones digit".) Hint: Use Euler's Theorem or Fermat's Little Theorem with p = 5, and remember that 3^100 will be an odd num      Log On


   

Question 848383: 4. Find the unit digit of 3^100. (The unit digit is the \ones digit".) Hint: Use Euler's
Theorem or Fermat's Little Theorem with p = 5, and remember that 3^100 will be an
odd number.
Questions are taken from the relevant sections of the textbook, An introduction
to Abstract Algebra with notes to the future teacher (Nicodemi, et. al.). This
week covers Sections 1.7, 2.1.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
The units digit of 3^100 is the remainder when dividing by 10.
So 3^100 (mod 10) is what we are looking for.
notice 3^2 = 9 = -1(mod 10)
3^(2n) = (-1)^n (mod 10)
3^(2*50) = (-1)^50 (mod 10)
Hence the remainder is 1.