I agree with Utgikar that the equation of state PV = nRT represents the definition of an ideal gas, according to the macroscopic viewpoint (no assumptions regarding the structure of matter). Nevertheless, there are several situations where some properties of a real gas are identical to those of the ideal gas. As stated in the paper, at Boyle's temperature and sufficiently low pressures, the virial equation of state becomes PV = RT, although some of the properties of the gas are different from those of the ideal gas. Similarly, at temperature T_H the enthalpy becomes independent of the pressure, although the gas is not ideal. Perhaps the message would be clearer if we write PV RT, to keep the strict definition of an ideal gas.