Number Theory

 

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

 

        17/17 = 1 R 0      

      103/17 = 6 R 1        73/17 = 4 R 5        43/17 = 2 R 9          47/17 = 2 R 13    

        19/17 = 1 R 2        23/17 = 1 R 6        61/17 = 3 R 10        31/17 = 1 R 14    

        37/17 = 2 R 3        41/17 = 2 R 7        79/17 = 4 R 11         83/17 = 4 R 15    

        89/17 = 5 R 4        59/17 = 3 R 8        29/17 = 1 R 12         67/17 = 3 R 16    

 

So, we can say, shown empirically, that all the possible     

remainders are every integer from 0 to 16, inclusive.    

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