document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136217>Question 136217</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0071244255/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Dear sir/madam,\r<BR>\n" );
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document.write( "I am stucked with the following problems and hope that you could guide me. \r<BR>\n" );
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document.write( "1. (a) Given c>0, prove that lcm(ac,bc)= clcm(a,b)<BR>\n" );
document.write( "   (b) Prove that one of any m consecutive integers must be divisible by m.\r<BR>\n" );
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document.write( "Thank you very much. \r<BR>\n" );
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document.write( "Best wishes,<BR>\n" );
document.write( "Mr Tan Guodong </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99797 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=99797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm not at all sure how to even approach the first one.  Perhaps someone else can help you.\r<BR>\n" );
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document.write( "But here is a rather intuitive discussion of the second problem:\r<BR>\n" );
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document.write( "If some integer p is divided by another integer m, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3E=m ALIGN=MIDDLE  ALT=\"p%3E=m\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using integer division, then there are exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m-1 ALIGN=MIDDLE  ALT=\"m-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible non-zero remainders.  If given m consectutive integers, dividing each by m will result in m different remainders.  Since there are only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m-1 ALIGN=MIDDLE  ALT=\"m-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > non-zero remainders available, one of the m remainders must be 0, hence one of the m integers is evenly divisible by m. </SPAN>\n" );
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