document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165100>Question 1165100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) Find the smallest positive integer which can be written as the sum of<BR>\n" );
document.write( "three, four, five or seven consecutive integers.<BR>\n" );
document.write( "(b) Explain why it is not possible for a number to be written as both<BR>\n" );
document.write( "the sum of four consecutive integers and the sum of six consecutive<BR>\n" );
document.write( "integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789561 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"Integers\" includes negative values, unless otherwise restricted.\r<BR>\n" );
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document.write( "-1 + 0 + 1 = 0  <BR>\n" );
document.write( "0 + 1 + 2 = 3    (3 is the smallest positive integer that is the sum of three consecutive integers)<br>\r<BR>\n" );
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document.write( "-1 + 0 + 1 + 2 = 2  (2 is the smallest positive integer that is the sum of four consecutive integers)<br>\r<BR>\n" );
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document.write( "etc.\r<BR>\n" );
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document.write( "5 consec. integers:  min sum gt zero = 5<br><BR>\n" );
document.write( "7 consec. integers:  min sum gt zero = 7<br> \r<BR>\n" );
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document.write( "(b) if  N = a + (a+1) + (a+2) + (a+3) = 4a + 6<BR>\n" );
document.write( "and   N = b + (b+1) + (b+2) + ... + (b+5) = 6b + 15<br>\r<BR>\n" );
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document.write( "then     6b + 15 = 4a + 6<BR>\n" );
document.write( "          6b + 9 = 4a<BR>\n" );
document.write( "         and  a = (6b + 9) / 4    \r<BR>\n" );
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document.write( "which is not an integer (6b is even, even + odd is odd, odd divided by 4 has a remainder) <br> \r<BR>\n" );
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document.write( "To the student:  Oh, I may have misread the question.  I see what you mean... perhaps the question should have been \"Find the smallest positive integer which can be written as the sum of three, four, five, AND seven consecutive numbers.\"   but OR makes sense too upon re-reading.  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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