Short Answer

Find four numbers congruent 5 modulo 17 .

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

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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.

$5 mod 17 \equiv 5 + 17 k mod 17 (for every integer k)$

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

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

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

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

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Discrete Mathematics and its Applications

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Short Answer

Find four numbers congruent 5 modulo 17 .

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Discrete Mathematics and its Applications

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Short Answer

Find four numbers congruent 5 modulo 17 .

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