Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1989. 19/8. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 19)

K. Dialek — A . Grytzuk: Some remarks on certain diophontine equations

(4.1) i a i + 1 + L I! x y z has a solution In positive integers x

fy,z for every n=>4k, 4k+2, 4k+3, Bk>5, where k=i,2,... The proof follows from the following identities: dl s + kxrhy + ck+t >nrr2T 4 _ 1 4k

+2 ~ nr+TTT^FfTT ~ CT? + ik+1 =2CkÍiy + nt+I>«Bk+53 + 2 THEOREM 4

. The equation Cd. 2) 5. o L + t + L n x y z has a solution in positive integers x,y,z for every n*=4k, dk+2, ak+3, where k-1,2,..» The proof follows from the following identities: 5 1 . 1 . 1 51? JT+T + ZTE" + ícTk+TT " krr + Tohvrs + rk+nrsrar SETS D k^T + SEiS + CTc+i>ak+3> •