SOLUTION: Prove that there are no positive integers x, y, z, t such that
x^2 + y^2 − 3z^2 −7t^2 = 0.
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
Pell's equation is solvable (x = 8 and t = 3 are the smallest known solutions.)
The negative Pell's equation is not known to be solvable in positive integers.
Hence the equation itself, formed by directly adding corresponding sides of the two Pell equations, is not solvable in positive integers x, y, z, and t.
RELATED QUESTIONS
Prove that there are no positive integers x, y, z, t such that
x^2 + y^2 − 7z^2... (answered by robertb)
Prove that there are no positive integers x, y, z such that
x^2+y^2 = 3z^2... (answered by ikleyn)
3y + 2z = 2
2x − y − 3z = 2
2x + 2y − z = 4
(x, y, (answered by Alan3354)
Find m (m < 0) such that y = mx − 7 has one intersection point with y = −m (x (answered by josgarithmetic)
Can someone help explain as, I'm confused to what the question is expecting the answer to (answered by stanbon,MathTherapy)
This is a calculus problem.
Consider two integers x and y such that x−y=12. What... (answered by richwmiller)
calculus. Consider two integers x and y such that x−y=12. What value of y will... (answered by stanbon)
This is a calculus problem. Consider two integers x and y such that x−y=12. What... (answered by Fombitz)
Prove:the sum of the squares of two odd integers cannot be a perfect square, i.e, if x... (answered by amarjeeth123)