The MSL Curiosity rover investigated dark, Mn-P-enriched nodules in shallow lacustrine/fluvial sediments at the Groken site in Glen Torridon, Gale Crater, Mars. Applying all relevant information from the rover, the nodules are interpreted as pseudomorphs after original crystals of vivianite, (Fe2+,Mn2+)3(PO4)2 center dot 8H2O, that cemented the sediment soon after deposition. The nodules appear to have flat faces and linear boundaries and stand above the surrounding siltstone. ChemCam LIBS (laser-induced breakdown spectrometry) shows that the nodules have MnO abundances approximately twenty times those of the surrounding siltstone matrix, contain little CaO, and have SiO2 and Al2O3 abundances similar to those of the siltstone. A deconvolution of APXS analyses of nodule-bearing targets, interpreted here as representing the nodules' non-silicate components, shows high concentrations of MnO, P2O5, and FeO and a molar ratio P/Mn = 2. Visible to near-infrared reflectance of the nodules (by ChemCam passive and Mastcam multispectral) is dark and relatively flat, consistent with a mixture of host siltstone, hematite, and a dark spectrally bland material (like pyrolusite, MnO2). A drill sample at the site is shown to contain minimal nodule material, implying that analyses by the CheMin and SAM instruments do not constrain the nodules' mineralogy or composition. The fact that the nodules contain P and Mn in a small molar integer ratio, P/Mn = 2, suggests that the nodules contained a stoichiometric Mn-phosphate mineral, in which Fe did (i.e., could) not substitute for Mn. The most likely such minerals are laueite and strunzite, Mn2+Fe3+2(PO4)2(OH)2 center dot 8H2O and -6H2O, respectively, which occur on Earth as alteration products of other Mn-bearing phosphates including vivianite. Vivianite is a common primary and diagenetic precipitate from low-oxygen, P-enriched waters. Calculated phase equilibria show Mn-bearing vivianite could be replaced by laueite or strunzite and then by hematite plus pyrolusite as the system became more oxidizing and acidic. These data suggest that the nodules originated as vivianite, forming as euhedral crystals in the sediment, enclosing sediment grains as they grew. After formation, the nodules were oxidized-first to laueite/strunzite yielding the diagnostic P/Mn ratio, and then to hematite plus an undefined Mn oxy-hydroxide (like pyrolusite). The limited occurrence of these Mn-Fe-P nodules, both in space and time (i.e., stratigraphic position), suggests a local control on their origin. By terrestrial analogies, it is possible that the nodules precipitated near a spring or seep of Mn-rich water, generated during alteration of olivine in the underlying sediments.