Part 1

  1. Write down + and * tables for Z_4
  2. Evaluate 2*(3*2+1) in Z_4
  3. Recall that "-x" denotes the additive inverse of x. For each element of Z_4 write its additive inverse (or N/A if it doesn't exist). 
    	    x | -x
	    ------
	    0 |
	    1 |
	    2 |
	    3 |
  4. Evaluate 3 - (-1 + 2*3) in Z_4
  5. Can (x - 1) + 3 = 0 be solved in Z_4?
  6. Recall what the multiplicative inverse is. We will denote the multiplicative inverse of $x$ as $x^{-1}$. For each element of Z_4 write its multiplicative inverse 
    	    x | x^(-1)
	    ---------
	    0 |
	    1 |
	    2 |
	    3 |
  7. Does 2 x + 1 = 0 have a solution in in Z_4?

Part 2

Here are the + and * tables for Z_11: 
 +  0  1  2  3  4  5  6  7  8  9 10
 0  0  1  2  3  4  5  6  7  8  9 10
 1  1  2  3  4  5  6  7  8  9 10  0
 2  2  3  4  5  6  7  8  9 10  0  1
 3  3  4  5  6  7  8  9 10  0  1  2
 4  4  5  6  7  8  9 10  0  1  2  3
 5  5  6  7  8  9 10  0  1  2  3  4
 6  6  7  8  9 10  0  1  2  3  4  5
 7  7  8  9 10  0  1  2  3  4  5  6
 8  8  9 10  0  1  2  3  4  5  6  7
 9  9 10  0  1  2  3  4  5  6  7  8
10 10  0  1  2  3  4  5  6  7  8  9
 
 *  0  1  2  3  4  5  6  7  8  9 10
 0  0  0  0  0  0  0  0  0  0  0  0
 1  0  1  2  3  4  5  6  7  8  9 10
 2  0  2  4  6  8 10  1  3  5  7  9
 3  0  3  6  9  1  4  7 10  2  5  8
 4  0  4  8  1  5  9  2  6 10  3  7
 5  0  5 10  4  9  3  8  2  7  1  6
 6  0  6  1  7  2  8  3  9  4 10  5
 7  0  7  3 10  6  2  9  5  1  8  4
 8  0  8  5  2 10  7  4  1  9  6  3
 9  0  9  7  5  3  1 10  8  6  4  2
10  0 10  9  8  7  6  5  4  3  2  1
  1. Evaluate 9*3 + 10 in Z_11
  2. What is -4 in Z_11?
  3. Evaluate 8*2 - 4 in Z_11
  4. Does 5 have a multiplicative inverse in Z_11
  5. Solve 5*x + 8 = 0 in Z_11