document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105540>Question 1105540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A series of 567 consecutive integers has a sum that is a perfect cube. Find the smallest possible positive sum for this series. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720383 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A series of 567 consecutive integers has a sum that is a perfect cube. Find the smallest possible positive sum for this series.<BR>\n" );
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document.write( "If zero is considered to be positive, the answer is zero (0).<BR>\n" );
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document.write( "If not:<BR>\n" );
document.write( "283 negative consecutive integers, then 0, then 283 positive consecutive integers has a sum of zero (0).<BR>\n" );
document.write( "Moving the start, the smallest integer up 1 adds 567 to the sum.<BR>\n" );
document.write( "567 = 21*27 = 21*3^3<BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%5E3%2A3%5E3 ALIGN=MIDDLE  ALT=\"21%5E3%2A3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the smallest sum.<BR>\n" );
document.write( "= 63^3<BR>\n" );
document.write( "= 250047<BR>\n" );
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