20x^6 + 10y^6 - 30z^6 = w^2 We show diophantine equation 20x^6 + 10y^6 - 30z^6 = w^2 has infinitely many integer solutions. 20x^6 + 10y^6 - 30z^6 = w^2.................................................(1) For details,ax^6 + by^6 + cz^6 = w^2 Ⅴ Let (a,b,c)=(20, 10, -30),(p,q)=(2, -1) the we obtain u^2 = 1260000000t^4+3600000000t^3+4500000000t^2+2400000000t+900000000........(2) This quartic equation is birationally equivalent to an elliptic curve below. Y^2 = X^3-165375X -14006250. Rank is 2 and generator is (X,y)=[-350,1000],[5482234150/491401,-405644379026750/344472101]. Hence we can obtain infinitely many integer solutions for equation (1). Numerical example: [X,Y,Z,W] = [977, 2417, 1457, 41522241600].

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