+743 Let $p$ be a prime. What are the possible remainders when $p$ is divided by $17?$ Select all that apply.
+302 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
