Problem 1. Evaluate the following expressions: (a) 8 (mod 3) = (d) 22 (mod 11) = (b) 17 (mod 8) = (e) −17 (mod 8) = (c) 7 (mod 12) = (f ) 0 (mod 9) =
Problem 1. Evaluate the following expressions:
(a) 8 (mod 3) =
(d) 22 (mod 11) =
(b) 17 (mod 8) =
(e) −17 (mod 8) =
(c) 7 (mod 12) =
(f ) 0 (mod 9) =
Problem 2. Evaluate the expressions in each of the following triples:
(a) 8 (mod 3) = 12 (mod 3) = 8 + 12 (mod 3) =
(b) 7 (mod 5) = 23 (mod 5) = 7 + 23 (mod 5) =
(c) 3 (mod 4) = 10 (mod 4) = 3 · 10 (mod 4) =
(d) 16 (mod 10) = 11 (mod 10) = 16 · 11 (mod 10) =
What conclusions can you draw?
Problem 3. Evaluate the following (please do not use a calculator): (a) 11 · 11 · 11 · 11 · 11 (mod 10) =
(b) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 (mod 2) =
(c) 2100 (mod 3)
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