document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=872663>Question 872663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that there exist some n<BR>\n" );
document.write( "such that<BR>\n" );
document.write( "(x^n)^2=x^n for all n>= 1.<BR>\n" );
document.write( "r is idemotent ring where x^2= x<BR>\n" );
document.write( "I have more this one is just to check who is qualified to help me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #526399 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=526399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r is idempotent ring where x^2 = x<BR>\n" );
document.write( "Prove there exists some n such that<BR>\n" );
document.write( "(x^n)^2 = x^n for all n>= 1<BR>\n" );
document.write( "now for n = 1, we have <BR>\n" );
document.write( "x^2 = x which is true for x a member of r<BR>\n" );
document.write( "for n+1 we need to show<BR>\n" );
document.write( "(x^n+1)^2 = x^n+1<BR>\n" );
document.write( "(x^n+1)^2 = (x^n * x)(x^n * x)<BR>\n" );
document.write( "(x^n+1)^2 = (x^n)^2 * x^2<BR>\n" );
document.write( "(x^n+1)^2 =  x^n * x<BR>\n" );
document.write( "(x^n+1)^2 =  x^n+1\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );