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Context. Gliese 832 (GJ 832) is an M2V star hosting a massive planet on a decade-long orbit, GJ 832b, discovered by radial velocity (RV). Later, a super Earth or mini-Neptune orbiting within the stellar habitable zone was reported (GJ 832c). The recently determined stellar rotation period (45.7 $\pm$ 9.3 days) is close to the orbital period of putative planet c (35.68 $\pm$ 0.03 days). Aims. We aim to confirm or dismiss the planetary nature of the RV signature attributed to GJ 832c, by adding 119 new RV data points, new photometric data, and an analysis of the spectroscopic stellar activity indicators. Additionally, we update the orbital parameters of the planetary system and search for additional signals. Methods. We performed a frequency content analysis of the RVs to search for periodic and stable signals. Radial velocity time series were modelled with Keplerians and Gaussian process (GP) regressions alongside activity indicators to subsequently compare them within a Bayesian framework. Results. We updated the stellar rotational period of GJ 832 from activity indicators, obtaining $37.5^{+1.4}_{-1.5}$ days, improving the precision by a factor of 6. The new photometric data are in agreement with this value. We detected an RV signal near 18 days (FAP < 4.6%), which is half of the stellar rotation period. Two Keplerians alone fail at modelling GJ 832b and a second planet with a 35-day orbital period. Moreover, the Bayesian evidence from the GP analysis of the RV data with simultaneous activity indices prefers a model without a second Keplerian, therefore negating the existence of planet c.