<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:16"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">m</font>,<font color="Maroon">n</font> <a href="int_2.html#R2">are_relative_prime</a> 
 ;<br/>

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:16"/><i><font color="Green">E31</font></i>: 
 ex <font color="Olive">i0</font>, <font color="Olive">j0</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">i0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">j0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>and </b><br/><a NAME="E4:16"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st  ex <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">j</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Olive">c</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) holds <br/><font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">c</font>
 <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">i0</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">j0</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E6:16"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">j0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span>
 <b>and </b><br/><a NAME="E7:16"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i/>;<br/>
<a NAME="E8:16"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st  ex <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">j</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Olive">c</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) holds <br/><font color="Olive">c</font> <a href="nat_1.html#K6">mod</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:16_1"/><i><font color="Green">E47</font></i>: 
 ex <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">j</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E2:16_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">b</font> <a href="nat_1.html#K6">mod</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>consider </b><font color="Maroon">i</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">j</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E4:16_1"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">t1</font> = <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i0</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">t2</font> = <font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">j0</font></span>)</span>;<br/>
<a NAME="E5:16_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K6">mod</a> <font color="Maroon">a</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T47">NAT_1:47</a></i>;<br/>
<a NAME="E6:16_1"/><b>then </b><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K6">mod</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E7:16_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">b</font> <a href="nat_1.html#K6">mod</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
;<br/>
<b>reconsider </b><font color="Maroon">c</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i0</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">j0</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, , <a class="txt" href="euler_1.html#E1"><i><font color="Green">Lemma27</font></i></a></i>;<br/>
<a NAME="E9:16_1"/>
<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font>
 
<b>by </b><i>, , , <a class="txt" href="euler_1.html#E1"><i><font color="Green">Lemma27</font></i></a>, <a class="ref" href="nat_1.html#T46">NAT_1:46</a></i>;<br/>
<b>hence </b><a NAME="E10:16_1"/>
contradiction
 <b>by </b><i>, , , , <a class="txt" href="euler_1.html#E1"><i><font color="Green">Lemma27</font></i></a>, <a class="txt" href="euler_1.html#E2"><i><font color="Green">Lemma28</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon">1'</font> = 1, <font color="Maroon">0'</font> = 0 as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<a NAME="E10:16"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_2_1"/>
( <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">m</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_2_1_1"><b>suppose </b></a><a NAME="E1:16_2_1_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:16_2_1_1"/>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T53">NAT_1:53</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_2_1_2"><b>suppose </b></a><a NAME="E1:16_2_1_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">m</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c</font> = <span class="p1">(<span class="default"><font color="Maroon">1'</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">0'</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><a NAME="E3:16_2_1_2"/>
<font color="Maroon">c</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i/>;<br/><a NAME="E4:16_2_1_2"/><b>then </b>
<font color="Maroon">m</font> <a href="nat_1.html#K6">mod</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/><a NAME="E5:16_2_1_2"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0
 <b>by </b><i>, <a class="ref" href="nat_1.html#T47">NAT_1:47</a></i>;<br/><b>hence </b><a NAME="E6:16_2_1_2"/>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T49">NAT_1:49</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E11:16"/>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_3_1"/>
( <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_3_1_1"><b>suppose </b></a><a NAME="E1:16_3_1_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:16_3_1_1"/>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T53">NAT_1:53</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_3_1_2"><b>suppose </b></a><a NAME="E1:16_3_1_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c</font> = <span class="p1">(<span class="default"><font color="Maroon">0'</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">1'</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><a NAME="E3:16_3_1_2"/>
<font color="Maroon">c</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i/>;<br/><a NAME="E4:16_3_1_2"/><b>then </b>
<font color="Maroon">n</font> <a href="nat_1.html#K6">mod</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/><a NAME="E5:16_3_1_2"/><b>then </b>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0
 <b>by </b><i>, <a class="ref" href="nat_1.html#T47">NAT_1:47</a></i>;<br/><b>hence </b><a NAME="E6:16_3_1_2"/>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T49">NAT_1:49</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E12:16"/><b>then </b>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#D5">NAT_1:def 5</a></i>;<br/>
<a NAME="E13:16"/><b>then </b>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> 1
 
<b>by </b><i>, <a class="ref" href="int_2.html#D6">INT_2:def 6</a></i>;<br/>
<a NAME="E14:16"/><b>then </b>
 ex <font color="Olive">b</font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>
<a NAME="E15:16"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">j0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T40">NAT_1:40</a></i>;<br/>
<b>then </b><font color="Maroon">k</font> = 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">j0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i0</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">j0</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span></span>)</span>

;<br/>
<a NAME="E17:16"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i0</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">j0</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E18:16"/>
 ex <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="int_1.html#NM1">Integer</a> st <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">j</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 ;<br/>


</div>
