  Time modulations at per mil level have been reported to take place in the
decay constant of several nuclei with period of one year (most cases) but also
of about one month or one day. On the other hand, experiments with similar or
better sensitivity have been unable to detect any modulation. In this letter we
give the results of the activity study of two different sources: 40K and 226Ra.
The two gamma spectrometry experiments have been performed underground at the
Gran Sasso Laboratory, this way suppressing the time dependent cosmic ray
background. Briefly, our measurements reached the sensitivity of 3.4 and 3.5
parts over 10^6 for 40K and 226Ra, respectively (1 sigma) and they do not show
any statistically significant evidence of time dependence in the decay
constant. We also give the results of the activity measurement at the time of
the two strong X-class solar flares which took place in September 2017. Our
data do not show any unexpected time dependence in the decay rate of 40K in
correspondence with the two flares. To the best of our knowledge, these are the
most precise and accurate results on the stability of the decay constant as
function of time.
