document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106806>Question 1106806</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If P(n,k)=120. Find the possible values of n and k. How many solutions are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721853 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=721853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor overlooked one solution....<br><BR>\n" );
document.write( "The values of P(n,k) are products of consecutive positive integers.  So we are looking for all ways we can get a product of 120 with consecutive positive integers.<br><BR>\n" );
document.write( "7 is not a factor of 120, so the largest positive integer we can use is 6.  And if we try using it, we find 6*5*4 = 120.  Three consecutive positive integers with the largest being 6 is P(6,3).<br><BR>\n" );
document.write( "What if we start with 5 as the largest positive integers?  We find 5*4*3*2 = 120; and then of course 5*4*3*2*1 is again 120.  These solutions correspond to P(5,4) and P(5,5).<br><BR>\n" );
document.write( "So there are three solutions to P(n,k) = 120: P(6,3), P(5,4), and P(5,5). </SPAN>\n" );
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