Solution for Section 3.4 Question 4

4. Recall that a b (mod d)   if  a mod d = r   and  b mod d = r,   that is, a and b leave the same remainder upon division by d. Note that this is the same as saying  a - b = kd  for some integer k or equivalently d | (a - b). 

i)   2 7 (mod 5)      True since 2 mod 5 = 2 and 7 mod 5 = 2.     You could also say that it is true since  5 | (2 - 7).

ii)   112 12 (mod 9)    False since 112 mod 9 = 4  and 12 mod 9 = 3.  You could also say that it is false since 9(112 - 12).

iii)   11² 7 (mod 3)     True since 121 mod 3 = 1 and 7 mod 3 = 1.   You could also say that it is true since  3 | (121 - 7).

Back to Section 3.4