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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K2">*</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>1</sub></font>

<br/>.= 
1 <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="newton.html#T64">NEWTON:64</a></i>
;<br/>
<b>hence </b><a NAME="E2:6"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="int_2.html#R2">are_relative_prime</a> 
 <b>by </b><i><a class="ref" href="int_2.html#D6">INT_2:def 6</a></i>;<br/>


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