An ohmic resistor is a resistor that obeys Ohm's law V = IR (voltage = current x resistance). Therefore, if the voltage in such element is increased by n number of times, by the same number n has to increase the current.
To determine if a resistor is ohmic, voltage in a resistor needs to be changed and both voltage and current have to be meassured. The obtained values are ploted on y = V(I) graph, if a line starting at 0 is obtained, then the measured properties are of an ohmic resistor and the gradient of the line is its resistance.