document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117931>Question 117931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is it possible for the remainder to be 2 when a prime number that is greater than 2 is divided by 4? Explain why or why not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85921 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is it possible for the remainder to be 2 when a prime number that is greater than 2 is divided by 4? Explain why or why not?<BR>\n" );
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document.write( "Is there a solution to x = 2(mod 4) if x is prime and greater than 2 ??<BR>\n" );
document.write( "If so there is an odd prime where 4 divides (x-2) with no remainder.<BR>\n" );
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document.write( "Argument:<BR>\n" );
document.write( "If x is odd, x-2 is odd <BR>\n" );
document.write( "But if x-2 is divisible by 4 it is a multiply of 2<BR>\n" );
document.write( "Then x-2 would be even.<BR>\n" );
document.write( "This contradiction means the assuption that there is<BR>\n" );
document.write( "an odd prime x where x= 2(mod 4) is wrong.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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