document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=404544>Question 404544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the equation is written to the base 3n-1 instead of base 10 (a,b,c) range from 0 to 3n-2 <BR>\n" );
document.write( "i have solved it up to the point but can't find a method to find a,b,c <BR>\n" );
document.write( "2[a(3n-1)^2 + b(3n-1) + c)] = c(3n-1)^2 + b(3n-1) + a<BR>\n" );
document.write( "a(18n^2 - 12n + 1) + b(3n-1) = c(9n^2 -6n -1)\r<BR>\n" );
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document.write( "(18a-9c)^2 + (-12a+3b+6c)n + (a+b+c) = 0\r<BR>\n" );
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document.write( "this is the bit where am stuck how to obtain a,b and c<BR>\n" );
document.write( "the answers should be a=n-1 b=3n-2 c=2n-1<BR>\n" );
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 #286001 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=286001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The easiest way is to try small cases (i.e. n = 1, 2, 3, etc.), then prove your result using induction. However there's quite a bit of algebra, and the only flaw is that the solution doesn't prove uniqueness. </SPAN>\n" );
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