document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=613270>Question 613270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In base, the number 31 represents a prime number. In base k, however, this two-digit number represents a perfect square. For what value or values of k, 3< k <10, is 31 a perfect square? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385923 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=385923\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In base, the number 31 represents a prime number. In base k, however, this two-digit number represents a perfect square. For what value or values of k, 3< k <10, is 31 a perfect square?<BR>\n" );
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document.write( "Assuming you mean base 10:<BR>\n" );
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document.write( "Bases 2 & 3 are eliminated by the 3.<BR>\n" );
document.write( "For bases 4 to 9, 31 = 3*b + 1, b is the base<BR>\n" );
document.write( "4: 13<BR>\n" );
document.write( "5: 16<BR>\n" );
document.write( "6: 19<BR>\n" );
document.write( "7: 22<BR>\n" );
document.write( "8: 25<BR>\n" );
document.write( "9: 28<BR>\n" );
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