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Found in: Page 307

### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

# Find four numbers congruent 5 modulo 17 .

The four possible numbers are 22, 39, 56, 73.

See the step by step solution

## Step 1

5 mod 17

All congruent numbers modulo 17 differ by a multiple of 17 , thus all numbers congruent to 5 modulo 17 are 5 increased by multiple of 17.

$5mod17\equiv 5+17kmod17\phantom{\rule{1em}{0ex}}\left(\text{for every integer}k\text{)}$

Let us evaluate 5 + 17k for a few values of k , for example k = 1,2,3,4

$\begin{array}{l}k=1 5+17k=5+17\left(1\right)=22\\ k=2 5+17k=5+17\left(2\right)=39\\ k=3 5+17k=5+17\left(3\right)=56\\ k=4 5+17k=5+17\left(4\right)=73\end{array}$

Thus four possible numbers are then 22, 39, 56, 73.

Note: If you use different k - values, then you obtain four different numbers.