document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89693>Question 89693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sorry! I put thwe wrong email address. The correct one is PayJ3@aol.com\r<BR>\n" );
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document.write( "\"Prove the product of 4 consecutive integers plus 1 is the square of an odd number (always)\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65169 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=65169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the first integer ... x(x+1)(x+2)(x+3)+1=x^4+6x^3+11x^2+6x+1 \r<BR>\n" );
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document.write( "since this is a perfect square and the coefficients of the first and last terms are 1, the factors must be of the form x^2+bx+1 \r<BR>\n" );
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document.write( "(x^2+bx+1)^2=x^4+2bx^3+(b^2+2)x^2+2bx+1 ... so b=3 ... x^2+3x+1=x(x+3)+1 \r<BR>\n" );
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document.write( "integers that are separated by an odd amount (3) must be odd and even; so their product must be even ... adding 1 makes it odd \r<BR>\n" );
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document.write( "ALWAYS </SPAN>\n" );
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