16x^6 + 9y^6 - 25z^6 = w^2 We show diophantine equation 16x^6 + 9y^6 - 25z^6 = w^2 has infinitely many integer solutions. 16x^6 + 9y^6 - 25z^6 = w^2.................................................(1) For details,ax^6 + by^6 + cz^6 = w^2 Ⅴ Let (a,b,c)=(16, 9, -25),(p,q)=(2, -7/9) the we obtain u^2 = 531968400t^4+1544702400t^3+1867698000t^2+1049760000t+354294000........(2) This quartic equation is birationally equivalent to an elliptic curve below. Y^2 = X^3-3470415X -1372046410. Rank is 1 and generator is (X,Y)=[-3243320666/2082249,-47937055961998/3004685307]. Hence we can obtain infinitely many integer solutions for equation (1). Numerical example: [X,Y,Z,W] = [34, 41, 7, 259740].

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