document.write( "Question 1207683: Let $p$ be a prime. What are the possible remainders when $p$ is divided by $17?$ Select all that apply. \n" ); document.write( "
Algebra.Com's Answer #845688 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Possible remainders are integers from 0 through 16, inclusive: \r\n" );
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document.write( "  P =  Q x 17 +  R\r\n" );
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document.write( " 17 =  1 x 17 +  0\r\n" );
document.write( "103 =  6 x 17 +  1\r\n" );
document.write( "  2 =  0 x 17 +  2\r\n" );
document.write( "  3 =  0 x 17 +  3\r\n" );
document.write( " 89 =  5 x 17 +  4\r\n" );
document.write( "  5 =  0 x 17 +  5\r\n" );
document.write( "193 = 11 x 17 +  6\r\n" );
document.write( "  7 =  0 x 17 +  7\r\n" );
document.write( " 59 =  3 x 17 +  8\r\n" );
document.write( "179 = 10 x 17 +  9\r\n" );
document.write( " 61 =  3 x 17 + 10\r\n" );
document.write( " 11 =  0 x 17 + 11\r\n" );
document.write( " 29 =  1 x 17 + 12\r\n" );
document.write( " 13 =  0 x 17 + 13\r\n" );
document.write( " 31 =  1 x 17 + 14\r\n" );
document.write( " 83 =  4 x 17 + 15\r\n" );
document.write( " 67 =  3 x 17 + 16\r\n" );
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document.write( "This might make you wonder if this is true:\r\n" );
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document.write( "For any prime t and any integer r, 0 < r < t-1,\r\n" );
document.write( "there will always be a prime p such that when \r\n" );
document.write( "p is divided by t, the remainder will be r.\r\n" );
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document.write( "We just proved it true for t=17.  \r\n" );
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document.write( "Edwin
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