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A large positive magnetoresistivity (up to tens of percents) is observed for both underdoped and overdoped superconducting La2-xSrxCuO4 epitaxial thin films at temperatures far above the superconducting critical temperature Tc. For the underdoped samples, this magnetoresistance far above Tc cannot be described solely by the Kohler effect and we believe it is to be attributed to the influence of superconducting fluctuations. In the underdoped regime, the large magnetoresistance is only observed when at low temperatures superconductivity occurs. The strong magnetoresistivity, which persists in some cases even at temperatures up to seven times Tc, can be related to the pairs forming the superconducting phase below Tc. Our observations support the idea of a close relation between the pseudogap and the superconducting gap and provide new indications for the presence of pairs above Tc.