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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th17</font></span>: <a NAME="T17"><span class="comment"><font color="firebrick">:: NAT_4:17</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">n</font>, <font color="Olive" title="b4">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b2">q</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  &amp; <font color="Olive" title="b4">d</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> &amp;  not <font color="Olive" title="b4">d</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <font color="Olive" title="b3">n</font></span>)</span> holds <br/><font color="Olive" title="b2">q</font> <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Olive" title="b4">d</font></div></div>
