document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620548>Question 620548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the largest 5-digit palindrome that is divisoble by 101. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390269 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=390269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose our palindrome is abcba, where a,b,c are digits, and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 101 | 10000a + 1000b + 100c + 10b + a\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 101 | 10001a + 1010b + 100c\">\r<BR>\n" );
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document.write( "1010b is already divisible by 101, so we can say that the above expression is equivalent to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 101 | 10001a + 100c\">\r<BR>\n" );
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document.write( "Modulo 101, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 10001 \equiv 2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 100 \equiv -1\">. Therefore,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2a - c \equiv 0 (mod 101)\">. Optimize and let a = 4, c = 8. Our choice of b doesn't matter, because 1010 is already 0 mod 101. Therefore, let b = 9. The largest palindrome multiple of 101 is\r<BR>\n" );
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document.write( "49894 </SPAN>\n" );
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