document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165285>Question 1165285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help me to solve this\r<BR>\n" );
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document.write( "Evaluate: Let Fz be the zth Fibonacci number where in z=x^2+y^2 such that  x and y are coprime integers between 2 and 6, inclusive.\r<BR>\n" );
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document.write( "Thank you in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789765 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Coprime integers are sets of integers such that 1 is the only positive integer that divides all elements of the set.  In this instance we are looking for 2-element subsets of the set {2, 3, 4, 5, 6} that are coprime.\r<BR>\n" );
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document.write( "Those two element sets are {2, 3}, {2, 5}, {3, 4}, {3, 5}, and {5, 6}\r<BR>\n" );
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document.write( "Now we want to find which of the above pairs of integers where the square of one added to the square of the other produces a Fibonacci number.\r<BR>\n" );
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document.write( "In review, the first twelve Fibonacci numbers are:\r<BR>\n" );
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document.write( "0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89\r<BR>\n" );
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document.write( "The sum of the squares of the elements of the two-element sets identified above:\r<BR>\n" );
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document.write( "4 + 9 = 13,  4 + 25 = 29, 9 + 16 = 25, 9 + 25 = 34, 25 + 36 = 61\r<BR>\n" );
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document.write( "Of these, only 13 and 34 are numbers in the Fibonacci sequence.\r<BR>\n" );
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document.write( "So the pairs you seek are {2, 3} and {3, 5}, hence x, y, z are either 2, 3, 13 or 3, 5, 34\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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