document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184232>Question 184232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that you square two consecutive whole numbers and subtract the smaller square from the larger. Is it possible that the difference is  an even number? Explain your answer with appropriate examples.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138262 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=138262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let k=first whole number, (ie k is NOT a fraction or decimal number)\r<BR>\n" );
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document.write( "So k+1 would be the next consecutive whole number\r<BR>\n" );
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document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B1 ALIGN=MIDDLE  ALT=\"k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B1%29%5E2=k%5E2%2B2k%2B1 ALIGN=MIDDLE  ALT=\"%28k%2B1%29%5E2=k%5E2%2B2k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2 ALIGN=MIDDLE  ALT=\"k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the square of the first number) from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%2B2k%2B1 ALIGN=MIDDLE  ALT=\"k%5E2%2B2k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the square of the second) to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%5E2%2B2k%2B1%29-k%5E2=%28k%5E2-k%5E2%29%2B2k%2B1=2k%2B1 ALIGN=MIDDLE  ALT=\"%28k%5E2%2B2k%2B1%29-k%5E2=%28k%5E2-k%5E2%29%2B2k%2B1=2k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now remember, we said at the top that \"k\" is a whole number. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k%2B1 ALIGN=MIDDLE  ALT=\"2k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is guaranteed to be an odd number (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k ALIGN=MIDDLE  ALT=\"2k\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an even integer)\r<BR>\n" );
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document.write( "So it is NOT possible to get an even difference between the squares of two consecutive whole numbers.\r<BR>\n" );
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document.write( "Examples (these don't prove the statement above, but help show it)\r<BR>\n" );
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document.write( "ex 1: Pick a number 6 and the next number 7. Square 6 to get 36. Square 7 to get 49\r<BR>\n" );
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document.write( "Subtract: 49-36=13\r<BR>\n" );
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document.write( "The difference is odd\r<BR>\n" );
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document.write( "ex 1: Select the number 12 and the next number 13. Square 12 to get 144. Square 13 to get 169\r<BR>\n" );
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document.write( "Subtract: 169-144=25\r<BR>\n" );
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document.write( "The difference is odd\r<BR>\n" );
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document.write( "You can try any two values and you'll find that the difference is odd.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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