LM317 Get Stable Output voltage at 1,25 V
Yes, as suggested, the LM317 DOES need a minimum load.   The specification
sheet suggests about 10 mA, LM317 see table 7.5 "minimum load current".

The bias current to run the internal error amplifier comes from the
input pin (#3 of the TO220 package) and the circuit is completed by output current at the output
pin (#2), while the sense pin (#1) carries only a small trickle of sense current.   If the R1 resistor is 120 ohms, it will be an adequate load resistance (R2 = zero ohms).    Lacking an adequate load, though,
the formula is inapplicable, because the internal amplifiers are lacking
the needed power supply current.