<p>There are many important facts that go along with Bezout’s identity:<br></p><div>1.)&nbsp;&nbsp;&nbsp;
All common divisors of <span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span> are common divisors of
<span class="ltx_Math" contenteditable="false" data-equation="a">\(a\)</span> and <span class="ltx_Math" contenteditable="false" data-equation="b">\(b\)</span> as well<br></div><div>2.)&nbsp;&nbsp;&nbsp; As for the fact above, all divisors of&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="a">\(a\)</span>&nbsp;and&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="b">\(b\)</span>&nbsp;are also divisors of&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span>.&nbsp;<br></div><div>3.)&nbsp;&nbsp;&nbsp;&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="a">\(a\)</span>/<span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span>&nbsp;and&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="b">\(b\)</span>/<span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span>&nbsp;are prime integers<br></div><div>4.) &nbsp; &nbsp;<span class="ltx_Math" contenteditable="false" data-equation="a">\(a\)</span>/<span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span><span class="ltx_Math" contenteditable="false" data-equation="\left(x\right)">\(\left(x\right)\)</span>+<span class="ltx_Math" contenteditable="false" data-equation="b">\(b\)</span>/<span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span><span class="ltx_Math" contenteditable="false" data-equation="\left(y\right)">\(\left(y\right)\)</span><span class="ltx_Math" contenteditable="false" data-equation="=1">\(=1\)</span><br></div><div>5.)&nbsp;&nbsp;&nbsp; The greatest common divisor&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span>&nbsp;is actually the smallest integer that can be written to satisy&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="ax+by">\(ax+by\)</span><br></div><div>6.)&nbsp;&nbsp;&nbsp; All integers of the form&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="ax+by">\(ax+by\)</span>&nbsp;are multiples of&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span><br></div>