document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=460663>Question 460663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Aliaba was arranging the carpets for the flying carpet brigade.  They were going to fly in a rectangular formation.  When he put 4 carpets in each row, he had 3 left over.  When he put 5 carpets in each row, he had 1 left over.  How many carpets could there have been in the carpet brigade?\r<BR>\n" );
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document.write( "Use more than one way to present your solution(s). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316001 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "To find the minimum number that has the characteristic that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ mod\ 4\ =\ 3\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ mod\ 5\ =\ 1\"> set:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 3}{4}\ =\ \frac{x\ -\ 1}{5}\">\r<BR>\n" );
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document.write( "And solve.  It should then be casual to the most obvious observer that since 4 times 5 is 20, that if you add any multiple of 20 to 11 you will get the same result.\r<BR>\n" );
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document.write( "Now we need to find a value <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 11\ +\ 20n\"> is non-prime.  That way, we can find a pair of integer factors and arrange the carpets in a rectangle with none left over.\r<BR>\n" );
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document.write( "11 is prime\r<BR>\n" );
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document.write( "31 is prime\r<BR>\n" );
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document.write( "51 NOT prime.  3 times 17 is a possible solution\r<BR>\n" );
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document.write( "71 is prime\r<BR>\n" );
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document.write( "91 NOT prime.  7 times 13...\r<BR>\n" );
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document.write( "There are infinitely more.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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