document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204795>Question 1204795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a,b,c,d, and e are distinct prime numbers such that: b=(a-1)^1/2 +1 ; c=(b-1)^1/2 +1 ; d=(c-1)^1/2 +1 ; e= (d-1)^1/2 +1 ; Find the least possible value of a+b+c+d+e<BR>\n" );
document.write( "A) 65537<BR>\n" );
document.write( "B) 65536<BR>\n" );
document.write( "C) 65816<BR>\n" );
document.write( "D) 65819<BR>\n" );
document.write( "E) 65814 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841287 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%28a-1%29%5E1%2F2+%2B1+ ALIGN=MIDDLE  ALT=\"b=%28a-1%29%5E1%2F2+%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=%28b-1%29%5E1%2F2+%2B1+ ALIGN=MIDDLE  ALT=\"c=%28b-1%29%5E1%2F2+%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%28c-1%29%5E1%2F2+%2B1+ ALIGN=MIDDLE  ALT=\"d=%28c-1%29%5E1%2F2+%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=+%28d-1%29%5E1%2F2+%2B1+ ALIGN=MIDDLE  ALT=\"e=+%28d-1%29%5E1%2F2+%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the least possible value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2Bb+%2Bc+%2Bd+%2Be ALIGN=MIDDLE  ALT=\"a+%2Bb+%2Bc+%2Bd+%2Be\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A Fermat number is of the form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large F_n\ =\ 2^2^n\,+\,1\">.<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%5Bn%5D ALIGN=MIDDLE  ALT=\"F%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > = { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large F_n\ =\ 2^2^4\,+\,1=65537\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large F_n\ =\2^2^3\,+\,1=257\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large F_n\ =\2^2^2\,+\,1=17\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large F_n\ =\2^2^1\,+\,1=5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large F_n\ =\2^2^0\,+\,1=3\">\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the five known prime Fermat numbers (in descending order)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65537 ALIGN=MIDDLE  ALT=\"65537\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=257 ALIGN=MIDDLE  ALT=\"257\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+17 ALIGN=MIDDLE  ALT=\"+17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "their sum is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65537%2B257%2B17%2B5%2B3=65819 ALIGN=MIDDLE  ALT=\"65537%2B257%2B17%2B5%2B3=65819\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "answer:\r<BR>\n" );
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document.write( "D) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65819 ALIGN=MIDDLE  ALT=\"65819\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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