document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=18148>Question 18148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is there any square number besides 9 and 81 that is divisible by 9?\r<BR>\n" );
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document.write( "-Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12829 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <p>Yes, lots of them. This is shown below</p>\r<BR>\n" );
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document.write( "<p>There is a theorem, called the fundamental theorem of arithmatic. Amongst other things it says that any whole number can be written as the product of primes. If we chose a number x, we can write it as this product of primes.</p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=p%5B1%5D%2Ap%5B2%5D%2Ap%5B3%5D%2A... ALIGN=MIDDLE  ALT=\"x=p%5B1%5D%2Ap%5B2%5D%2Ap%5B3%5D%2A...\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<p>Now consider <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and much more interestingly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E2 ALIGN=MIDDLE  ALT=\"%283x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.</p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=3%2Ap%5B1%5D%2Ap%5B2%5D%2Ap%5B3%5D%2A... ALIGN=MIDDLE  ALT=\"3x=3%2Ap%5B1%5D%2Ap%5B2%5D%2Ap%5B3%5D%2A...\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E2=3%2A3%2Ap%5B1%5D%2Ap%5B1%5D%2Ap%5B2%5D%2Ap%5B2%5D%2Ap%5B3%5D%2Ap%5B3%5D%2A... ALIGN=MIDDLE  ALT=\"%283x%29%5E2=3%2A3%2Ap%5B1%5D%2Ap%5B1%5D%2Ap%5B2%5D%2Ap%5B2%5D%2Ap%5B3%5D%2Ap%5B3%5D%2A...\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E2=9%2Ap%5B1%5D%2Ap%5B1%5D%2Ap%5B2%5D%2Ap%5B2%5D%2Ap%5B3%5D%2Ap%5B3%5D%2A... ALIGN=MIDDLE  ALT=\"%283x%29%5E2=9%2Ap%5B1%5D%2Ap%5B1%5D%2Ap%5B2%5D%2Ap%5B2%5D%2Ap%5B3%5D%2Ap%5B3%5D%2A...\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<p>As you can see <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E2 ALIGN=MIDDLE  ALT=\"%283x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a square number divisible by 9. I've just realised we didn't actually need the stuff about the primes, but it's good to learn something new everyday :D</p>\r<BR>\n" );
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document.write( "<p>For your enjoyment, here are three really big square numbers divisible by 9 that I worked out</p>\r<BR>\n" );
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document.write( "<li>290865928967208697537677954155146591215027084823761634916418981868464451672735642563258575025</li><BR>\n" );
document.write( "<li>377757024764443692555739771423286715885160196068990002369</li><BR>\n" );
document.write( "<li>287239467617910266150742450417499640849213343093880946478917496351351184155930613119360893088100381830756</li><BR>\n" );
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document.write( "<p>Hope that helps</p>\r<BR>\n" );
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document.write( "<p>Kev</p> </SPAN>\n" );
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