document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018809>Question 1018809</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find all natural n such that n^2 &#8722; 1 is a cube of a prime number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634843 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=634843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since n^2 - 1 factors to (n-1)(n+1), which is a cube of a prime number, either n-1 = 1 and n+1 = p^3, or n-1 = p and n+1 = p^2. Checking, we see that the only possible value of n is n = 3 (3^2 - 1 = 2^3). </SPAN>\n" );
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