As near as I can tell, this proof would work in any well-ordered integral domain D where D&#x27;s field of fractions would the role of the rationals.  The analogue of the standard proof would require that D also be a unique factorization domain (or maybe the slightly weaker condition that any two elements have a GCD).<p>It might be the case that all these properties together &quot;force&quot; D to be a UFD or that the author snuck another property of the integers in there, but I&#x27;ve only taken a cursory look.