document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550956>Question 550956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> here is my query...\r<BR>\n" );
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document.write( "Let a(x); b(x) and c(x) be polynomials with complex coeffcients such that<BR>\n" );
document.write( "gcd(a(x); b(x); c(x)) = 1<BR>\n" );
document.write( "(i.e. no polynomial of degree >= 1 divides all the three) and deg(a).deg(b).deg(c) =0<BR>\n" );
document.write( "0. Prove that,<BR>\n" );
document.write( "a(x)<BR>\n" );
document.write( "^n + b(x)<BR>\n" );
document.write( "^n != c(x)<BR>\n" );
document.write( "^n<BR>\n" );
document.write( "for all n >= 3\r<BR>\n" );
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document.write( "(!= => \"not equal to\") </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359617 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=359617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Unless I'm mis-interpreting your question, if deg(a)*deg(b)*deg(c) = 0, then one of the polynomials must be a constant.\r<BR>\n" );
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document.write( "If alpha, beta, gamma are the constant terms of each polynomial, then by equating constant terms on both sides, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \alpha^n + \beta^n = \gamma^n\">\r<BR>\n" );
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document.write( "However, alpha, beta, gamma have to be positive integers for Fermat's Last Theorem to apply. Your polynomials have complex coefficients, so you'll be in for a long run... </SPAN>\n" );
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