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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th7</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: HILB10_1:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n1</font>, <font color="Olive" title="b2">n2</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">a</font> being   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">n1</font>,<font color="Olive" title="b2">n2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is    <a href="pells_eq.html#M1" title="PELLS_EQ:mode.1">Pell's_solution</a> of <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 holds <br/> ex <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b1">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hilb10_1.html#K1" title="HILB10_1:func.1">Px</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">n</font>) &amp; <font color="Olive" title="b2">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hilb10_1.html#K2" title="HILB10_1:func.2">Py</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">n</font>) )</div></div>
