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

Question 1207683: Let $p$ be a prime. What are the possible remainders when $p$ is divided by $17?$ Select all that apply.
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Possible remainders are integers from 0 through 16, inclusive: 

  P =  Q x 17 +  R
------------------
 17 =  1 x 17 +  0
103 =  6 x 17 +  1
  2 =  0 x 17 +  2
  3 =  0 x 17 +  3
 89 =  5 x 17 +  4
  5 =  0 x 17 +  5
193 = 11 x 17 +  6
  7 =  0 x 17 +  7
 59 =  3 x 17 +  8
179 = 10 x 17 +  9
 61 =  3 x 17 + 10
 11 =  0 x 17 + 11
 29 =  1 x 17 + 12
 13 =  0 x 17 + 13
 31 =  1 x 17 + 14
 83 =  4 x 17 + 15
 67 =  3 x 17 + 16

This might make you wonder if this is true:

For any prime t and any integer r, 0 < r < t-1,
there will always be a prime p such that when 
p is divided by t, the remainder will be r.

We just proved it true for t=17.  

Edwin

RELATED QUESTIONS
(a) Let p be a prime number greater than 3. What are the possible remainders of p upon... (answered by jim_thompson5910)

P is a Four digit Prime number When Divided by 12 What Will be the Remainder?? (answered by richard1234)

When polynomial P(x) is divided by x + 1, x + 2, and x + 3, the remainders are 2, 3, and... (answered by Edwin McCravy,ikleyn)

1. Let v be the vector (3 over p), such that |v| = 17. Calculate all possible values of... (answered by stanbon)

Suppose that we have a sample space S {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, ..., E7 (answered by stanbon)

Let p and q be two positive numbers where p > q. Geoffrey graphs the numbers p, q, and... (answered by greenestamps)

1.)When the expression x^3+mx^2+nx-5 is divided by x+2 and x+3, the remainders are 2 and... (answered by KMST)

Topic:factors and multiples Qn) when 2power256 is divided by 17 the remainder would... (answered by josgarithmetic)

Let n ounces of a 15% acid solution be mixed with m ounces of a 55% salt solution. Which... (answered by ikleyn)