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Zak wrote:the fourh exponent is not too big?
Zak wrote:O.K. but if there are a lot of other solutions, why we can't to find at least one of them until at least 2^53 after all
x3mEn wrote:With the help of strict math logic of equivalent expressions you transfered from the given system of 4 Diophantine equations to consequent (and, btw, not necessary equivalent to input system) expression, which says: "If the given system of equations has a solution over integers, then the consequent expression is true over those values of system solutions.
Zak wrote:Decision of equation in integers will be equal to full task, because if we will have d,e,f, then we can find all the rest. We can find g and then we can find a,b,c.
I know about you had showed. But I told about other equation whith new integer variable x, which included sqr(16a^2b^2c^2g^2). The equation will be TRUE only in case when d,e,f will correspond perfect brick's face diagonals.
By means of transformations and finding the roots of the equation, we simply excluded cases that are not of interest to us.
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