Say that  .
Note that  .
Thus,  .
Our goal now is to show either  . Now  follows at once from the equation  . But if  we will show this implies that  .
Now if  then  . Thus,  .
Now we have established that  .
Say the first one is true  . Then  . But since  . Say therefore that  . Substitute  into  we get  . But then  .
Now using a similar argument with  we find that  .
I hope you like this proof. I really find it beautiful how divisibility arguments lead us to this conclusion.
__________________ We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America. |