document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27147>Question 27147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Formulate a conjecture for which natural number n the formula <BR>\n" );
document.write( "(a+b)^(n) = a^n + b^n holds in clock n. I don't have to prove the conjecture, just state it and suffices to consider clock n for n< and equal to 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15271 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING EXAMPLE<BR>\n" );
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document.write( "(a+b)^7 = a^7 + b^7 in clock 7<BR>\n" );
document.write( "IN CLOCK 7 THE NUMBERS REPEAT CHANGE DIGITS AFTER 7<BR>\n" );
document.write( "THAT IS 12=5(MOD7)...NUMBER TWELVE WILL BE REPRESENTED BY 5 THE REMAINDER AFTER DIVIDING 12 BY 7.<BR>\n" );
document.write( "LET A=X(MOD7)......................I<BR>\n" );
document.write( "AND B=Y(MOD7).......................II.......WHERE X AND Y ARE LESS THAN 7.<BR>\n" );
document.write( "A+B=(X+Y)(MOD7).............FROM I+II<BR>\n" );
document.write( "(A+B)^7={(X+Y)+(X+Y)+....7 TIMES}(MOD7)=7(X+Y)(MOD7)=(X+Y)(MOD7)............III <BR>\n" );
document.write( "A^7=(X+X+X...7 TIMES)(MOD7)=(7X)(MOD7)=X(MOD7)......FROMM I ................IV<BR>\n" );
document.write( "SIMILARLY..B^7=Y(M0D7).............FROM II..................................V<BR>\n" );
document.write( "ADDING IV AND V WE GET <BR>\n" );
document.write( "A^Y+B^7=X(M0D7)+Y(MOD7)=(X+Y)(MOD7).................................VI<BR>\n" );
document.write( "HENCE FROM III AND VI WE GET <BR>\n" );
document.write( "(a+b)^7 = a^7 + b^7 in clock 7 \r<BR>\n" );
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document.write( " </SPAN>\n" );
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