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Let p be a prime number greater than five. In the p -local stable homotopy groups of spheres, H Toda and J Lin, respectively, constructed the elements s 2 2sp 3 2p 2 2p 2sC1 .S/; ! m;n 2 2p nC1 2p n C2p mC1 2p m C2p 6 .S / of order p . In this paper, we show the nontriviality of the Toda bracket h s ; p; ! m;n i in the stable homotopy groups of spheres, where n > m C 2 > 6, 3 6 s < p . 55Q45, 55T15; 55S10doi:10.2140/agt.2009.9.221 fatcat:iq3x2cnmrnbqvg4qftpdgzqqj4