document.write( "Question 176318: 4) A student claims “If d does not divide a and d does not divide b, then d does not divide (a+b). How do you respond? Hint look in chapter 4. \n" ); document.write( "

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The modulo (x mod y) function provides the remainder when one integer (x) is divided by another (y). So if d does not divide a, then a mod d is non-zero. Also, if d does not divide b, then b mod d is non-zero. However, it is possible that (a mod d) + (b mod d) = kd where k is a non-zero positive integer. \r
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\n" ); document.write( "\n" ); document.write( "Further (a + b) mod d = (a mod d) + (b mod d) so (a + b) is divisible by d whenever (a mod d) + (b mod d) = kd. \n" ); document.write( "

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