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<b>let </b><font color="Maroon">i1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i2</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i5</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i3</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>







<b>assume </b><a NAME="E1:56"/>
( <font color="Maroon">i1</font>,<font color="Maroon">i2</font> <a href="int_1.html#R1">are_congruent_mod</a> <font color="Maroon">i5</font> &amp; <font color="Maroon">i1</font>,<font color="Maroon">i3</font> <a href="int_1.html#R1">are_congruent_mod</a> <font color="Maroon">i5</font> )
 ;<br/>

<a NAME="E2:56"/><b>then </b><i><font color="Green">E44</font></i>: 
( <font color="Maroon">i2</font>,<font color="Maroon">i1</font> <a href="int_1.html#R1">are_congruent_mod</a> <font color="Maroon">i5</font> &amp; <font color="Maroon">i3</font>,<font color="Maroon">i1</font> <a href="int_1.html#R1">are_congruent_mod</a> <font color="Maroon">i5</font> )
 
<b>by </b><i><a class="ref" href="int_1.html#T35">INT_1:35</a></i>;<br/>
<b>then consider </b><font color="Maroon">t1</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E4:56"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">i5</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="int_1.html#D3">INT_1:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon">t2</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E6:56"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">i5</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">t2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i3</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="txt" href="pepin.html#E4:56"><i><font color="Green">E45</font></i></a>, <a class="ref" href="int_1.html#D3">INT_1:def 3</a></i>;<br/>
<a NAME="E7:56"/>
<font color="Maroon">i2</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i5</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">t2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pepin.html#E2"><i><font color="Green">Lemma46</font></i></a>, <a class="txt" href="pepin.html#E3"><i><font color="Green">Lemma47</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:56"/>
<font color="Maroon">i2</font>,<font color="Maroon">i3</font> <a href="int_1.html#R1">are_congruent_mod</a> <font color="Maroon">i5</font>
 <b>by </b><i><a class="ref" href="int_1.html#D3">INT_1:def 3</a></i>;<br/>


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