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Let $p$ be a prime.  What are the possible remainders when $p$ is divided by $17?$  Select all that apply.

 Jul 1, 2024
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Let remainder to be r

And k to be a non-negative integer.

Set equation: p = 17k + r

The answer would be: \(\boxed{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}\)

To check: 

r = 0, k = 1

r = 1, k = 6

r = 2, k = 0

r = 3, k = 0

r = 4, k = 5

r = 5, k = 0

r = 6, k = 1

r = 7, k = 0 

r = 8, k = 3

r = 9, k = 2

r = 10, k = 3

r = 11, k = 0

r = 12, k = 1

r = 13, k = 0

r = 14, k = 1

r = 15, k = 4

r = 16, k = 3


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