Two scenarios have been proposed to account for sustained $ge 30$,MeV gamma-ray emission in solar flares: (1) prolonged particle acceleration/trapping involving large-scale magnetic loops at the flare site, and (2) precipitation of high-energy ($>$ 300 MeV) protons accelerated at coronal/interplanetary shock waves. To determine which of these scenarios is more likely, we examine the associated soft X-ray flares, coronal mass ejections (CMEs), and solar energetic proton events (SEPs) for: (a) the long-duration gamma-ray flares (LDGRFs) observed by the Large Area Telescope (LAT) on Fermi, and (b) delayed and/or spatially-extended high-energy gamma-ray flares observed by the Gamma-ray Spectrometer on the Solar Maximum Mission, the Gamma-1 telescope on the Gamma satellite, and the Energetic Gamma-Ray Experiment Telescope on the Compton Gamma-Ray Observatory. For the Fermi data set of 11 LDGRFs with $>$100 MeV emission lasting for $ge sim 2$ hours, we search for associations and reverse associations between LDGRFs, X-ray flares, CMEs, and SEPs, i.e., beginning with the gamma-ray flares and also, in turn, with X-class soft X-ray flares, fast ($ge$ 1500 km s$^{-1}$) and wide CMEs, and intense (peak flux $ge 2.67 times 10^{-3}$ protons cm$^{-2}$ s$^{-1}$ sr$^{-1}$, with peak to background ratio $>$ 1.38) $>$ 300 MeV SEPs at 1 A.U. While LDGRFs tend to be associated with bright X-class flares, we find that only 1/3 of the X-class flares during the time of Fermi monitoring coincide with an LDGRF. However, nearly all fast, wide CMEs are associated with an LDGRF. These preliminary association analyses favor the proton precipitation scenario, although there is a prominent counter-example of a potentially magnetically well-connected solar eruption with $>$ 100 MeV emission for $sim 10$ h for which the near-Earth $>$ 300 MeV proton intensity did not rise above background.
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