Let X, Y, Z be any positive integral solutions of this equation, and let H be the G.C.D. of X, Y. Then X = Hx, Y =Hy, Z = H2z, and (1) 2x4 - y4 = z2, where x, y, z are odd and co-prime in pairs. Hence it suffices to find primitive solutions x, y. z.
Proceedings of the Iowa Academy of Science
©1935 Iowa Academy of Science, Inc.
Turner, J. S.
"A Short Solution of the Diophantine Equation 2x^4 - Y^4 = Z^2,"
Proceedings of the Iowa Academy of Science, 42(1), 147-148.
Available at: https://scholarworks.uni.edu/pias/vol42/iss1/56