There do not exist positive integers x,y,z satisfying 2xz=y^2 & x+z=997

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- Jun 8th 2013, 04:58 AMswarnaNumber Theory
There do not exist positive integers x,y,z satisfying 2xz=y^2 & x+z=997

- Jun 14th 2013, 03:36 PMPhantasmaRe: Number Theory
Is there a...question?

- Jun 14th 2013, 08:54 PMibduttRe: Number Theory
Proceed by using these two equations to form a quadratic equation. Since we have two equations and three variables we cannot have a unique solution. we will get infinitely many solutions.

from first one we have z = (y^2)/(2x) plug in this in equation 2, we get

x + (y^2)/(2x) = 997

Form this quadratic and then try and reason out - Jun 15th 2013, 03:49 AMIdeaRe: Number Theory