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