document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=494495>Question 494495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following proposition: There are no integers a and b such that<BR>\n" );
document.write( "b^2 = 4a + 2.<BR>\n" );
document.write( "(a) Rewrite this statement in an equivalent form using a universal quantifier<BR>\n" );
document.write( "by completing the following:<BR>\n" );
document.write( "For all integers a and b,....<BR>\n" );
document.write( " (b) Prove the statement in Part (a).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335733 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=335733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You could say something like, \"For all integers a and b, b^2 is never equal to 4a+2.\"\r<BR>\n" );
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document.write( "For any integer b, b^2 is congruent to either 0 or 1 modulo 4. 4a+2 is always 2 modulo 4. If b^2 and 4a+2 were equivalent mod 4, then they could be equal but they're different mod 4, so they can never be equal. </SPAN>\n" );
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