document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016954>Question 1016954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let Dn denote the set of natural numbers that divide n exactly. For example,<BR>\n" );
document.write( "D60 = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}.<BR>\n" );
document.write( "Write down the sets D84 and D60 &#8746; D84. Find the number m such that Dm = D60 &#8746; D84. Is it true that for any natural numbers r and s there is a natural number m such that Dm = Dr &#8746; Ds?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #633303 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=633303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D_{84} = (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 56, 84 )\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D_{60} \cup D_{84} = (1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 60, 84 )\"> (should be {...} but this site doesn't recognize \{...\} for brackets)\r<BR>\n" );
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document.write( "I don't know if you typed your question correctly or incorrectly, but there is no positive integer m such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D_m = D_{60} \cup D_{84}\">. The reason is because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large m \in D_m\"> and m is necessarily the largest number in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D_m\">, but m cannot equal 84. </SPAN>\n" );
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