10x^6 + 2y^6 - 12z^6 = w^2 We show diophantine equation 10x^6 + 2y^6 - 12z^6 = w^2 has infinitely many integer solutions. 10x^6 + 2y^6 - 12z^6 = w^2.................................................(1) For details,ax^6 + by^6 + cz^6 = w^2 Ⅴ Let (a,b,c)=(10, 2, -12),(p,q)=(2, -4) the we obtain u^2 = 564480t^4-668160t^3+633600t^2-76800t+57600............................(2) This quartic equation is birationally equivalent to an elliptic curve below. Y^2 = -3243375X -1066196250. Rank is 3 and generator is (X,Y)=[ -1550,15400],[11650,1241900],[24830950/12321,-33015093650/1367631]. Hence we can obtain infinitely many integer solutions for equation (1). Numerical example: [X,Y,Z,W] = [55, 487, 127, 163190160].

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