Question 1030744
Pell's equation {{{x^2 - 7t^2 = 1}}} is solvable (x = 8 and t = 3 are the smallest known solutions.)

The negative Pell's equation {{{y^2 - 3z^2 = -1}}} is not known to be solvable in positive integers.

Hence the equation {{{x^2 + y^2 - 3z^2 - 7t^2 = 0}}} itself, formed by directly adding corresponding sides of the two Pell equations, is not solvable in positive integers x, y, z, and t.