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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="IntXGcd"></a>
IntXGcd
</h2>

Extended Euclidean algorithm.

<p><p>

<h3>
Syntax:
</h3>
<pre>G := IntXGcd (a1,a2);
G := IntXGcd (L);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  G  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  a1  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  a2  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#IntGcd">IntGcd</a>

<p>

<h3>
Description:
</h3>
The <tt> IntXGcd</tt> function computes the greatest common divisor
g of integers a_1, &hellip; ,a_n. g is the first element
of the list <tt> G</tt> which will be returned by <tt> IntXGcd</tt>.
The second element of <tt> G</tt> is another list which contains
the representation of g by a_1, &hellip; ,a_n.\medskip

<tt> IntXGcd (a1,a2);</tt>
computes the greatest common divisor of a_1, a_2
and its representation.\smallskip

<tt> IntXGcd (L);</tt>
Let L be a list of rational
integers a_1, &hellip; ,a_n. The <tt> IntXGcd</tt>
computes the greatest common divisor of a_1, &hellip; ,a_n
and its representation.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> G := IntXGcd(2345,-505);
[ 5, [ 14, 65 ] ]
kash> G[2][1]*2345+G[2][2]*(-505);
5
kash> G := IntXGcd([12,18,21]);
[ 3, [ 3, -3, 1 ] ]
kash> G[2][1]*12+G[2][2]*18+G[2][3]*21;
> 3

</pre>

<p>


<hr>

<p>
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