document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132162>Question 1132162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Fq ALIGN=MIDDLE  ALT=\"p%2Fq\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a fraction in lowest terms, must <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2%2Fq%5E2 ALIGN=MIDDLE  ALT=\"p%5E2%2Fq%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > be in lowest terms also? How about<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p+%2B+a%29%2F%28q+%2B+a%29 ALIGN=MIDDLE  ALT=\"%28p+%2B+a%29%2F%28q+%2B+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749103 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(a) Yes.  If p/q is in lowest terms, then p and q have no common divisors.<br><BR>\n" );
document.write( "In that case, p^2/q^2 = (p*p)/(q*q) will also have no common divisors.<br><BR>\n" );
document.write( "(b) No, of course not.  It is easy to find counterexamples.<br><BR>\n" );
document.write( "5/7 is in lowest terms; (5+1)/(7+1) = 6/8 is not. </SPAN>\n" );
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