document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252536>Question 252536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different values of n are there such that n is a natural number and <BR>\n" );
document.write( "n^2 - 20 is a perfect square?\r<BR>\n" );
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document.write( "(a) 1 (b) 2 (c) 3 (d) 4 (e) infinitely many </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184531 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How many different values of n are there such that n is a natural number and <BR>\n" );
document.write( "n^2 - 20 is a perfect square?<BR>\n" );
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document.write( "(a) 1 (b) 2 (c) 3 (d) 4 (e) infinitely many<BR>\n" );
document.write( " <BR>\n" );
document.write( "There are 2, +6 and -6.<BR>\n" );
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document.write( "a^2 - b^2 = 20<BR>\n" );
document.write( "(a-b)*(a+b) = 20<BR>\n" );
document.write( "This is one eqn in two variables, but restricted to integers.<BR>\n" );
document.write( "20 = 1*20, 2*10 or 4*5<BR>\n" );
document.write( "1 and 20<BR>\n" );
document.write( "a-b = 1<BR>\n" );
document.write( "a+b = 20  Not integers<BR>\n" );
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document.write( "2 and 10<BR>\n" );
document.write( "a-b = 2<BR>\n" );
document.write( "a+b = 10<BR>\n" );
document.write( "--> 4 and 6 which works<BR>\n" );
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document.write( "4 and 5 no integer solution<BR>\n" );
document.write( "6^2 - 20 = 4^2<BR>\n" );
document.write( "(-6)^2 - 20 = 4^2<BR>\n" );
document.write( "No other solutions. </SPAN>\n" );
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