SOLUTION: Prove that there are no positive integers x, y, z, t such that x^2 + y^2 − 3z^2 −7t^2 = 0.

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Question 1030744: Prove that there are no positive integers x, y, z, t such that
x^2 + y^2 − 3z^2 −7t^2 = 0.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Pell's equation x%5E2+-+7t%5E2+=+1 is solvable (x = 8 and t = 3 are the smallest known solutions.)
The negative Pell's equation y%5E2+-+3z%5E2+=+-1 is not known to be solvable in positive integers.
Hence the equation x%5E2+%2B+y%5E2+-+3z%5E2+-+7t%5E2+=+0 itself, formed by directly adding corresponding sides of the two Pell equations, is not solvable in positive integers x, y, z, and t.