document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=923017>Question 923017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the remainder when the sum 1^99 + 2^99 + 3^99........+ 2014^99 is divided by 2015?\r<BR>\n" );
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document.write( "Thank you for your answer :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559823 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=559823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In general, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large k^{99} + (2015 - k)^{99} \equiv k^{99} + (-k)^{99} \equiv 0\"> (mod 2015)\r<BR>\n" );
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document.write( "Therefore 1^99 + 2014^99 is divisible by 2015, 2^99 + 2013^99 is divisible by 2015, ..., 1007^99 + 1008^99 is divisible by 2015, so the total remainder is 0. </SPAN>\n" );
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