document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4726>Question 4726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that 5n+3 and 7n+ 4 are relatively prime for all n </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2311 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Use the fact about gcd:<BR>\n" );
document.write( "  d=(a,b) if and only if there exist integer p, q such that<BR>\n" );
document.write( "  pa + qb = d.\r<BR>\n" );
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document.write( " Hence, (a,b) = 1 if  and only if there exist integer p, q such that<BR>\n" );
document.write( "  pa + qb = 1.\r<BR>\n" );
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document.write( " Now, 3(5n+3)-2(7n+ 4) = 15n + 9 -14n- 8 = 1<BR>\n" );
document.write( " So, (5n+3, 7n+ 4) = 1 ie (5n+3 ) and (7n+ 4) are relative prime for all n.\r<BR>\n" );
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document.write( " Another way of proof:<BR>\n" );
document.write( " if d =(5n+3, 7n+4), consider 7(5n+3)-5(7n+4) = 1,<BR>\n" );
document.write( " since d is a divisor of 7(5n+3)-5(7n+4),<BR>\n" );
document.write( " d must be 1 and so (5n+3 ) and (7n+ 4)are relative prime. \r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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