Question on: SS1 Mathematics - Modular Arithmetic
Convert 34 and −34 to their congruent values in mod 9
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(a) \(34\ (mod\ 9)\ \equiv x\)
\[\frac{34}{9} = 3\ remainder\ \mathbf{7}\]
Thus, \(34\ (mod\ 9)\ \equiv \mathbf{7}\)
(b) \(- 34\ (mod\ 9)\ \equiv x\)
\[- 34 = x\ (mod\ 9)\ \ \]
\[- 34 = q.9 + x\]
\[- 34 = \ - 4(9) + x\]
\[- 34 = - 36 + x\]
\[- 34 + 36 = x\]
\[x = \mathbf{2}\]
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