Diophantine equation


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Diophantine equation

(mathematics)
Equations with integer coefficients to which integer solutions are sought. Because the results are restricted to integers, different algorithms must be used from those which find real solutions.

References in periodicals archive ?
The Diophantine equation x8 + y3 = z4 has no relatively prime positive integer solutions.
Diophantine equation (3) for the first order systems without the time delay can be easily transformed into polynomial equation:
Mollin, Generalized Lagrange criteria for certain quadratic Diophantine equations, New York J.
ps] by a general solution of a stabilizing Diophantine equation.
Keywords Lattice point, lattice triangle, lattice cubic, Diophantine equation
For example, the famous Fermat's last theorem is that the Diophantine equation
The basic Diophantine equation for the stabilization problem in the ring of polynomials can be read as
From these two equations, we get the Diophantine equation
The problem how to solve the Diophantine equation, a special case of which is the above one, is considered in Theorem 110 from [13].
Moreover, the Diophantine equation approach gives a scalar tuning parameter which can be adjusted by various principles.
We also show that the Diophantine equation (The generalized Fermat-Catalan equation)
Keywords Smarandache function; Pseudo Smarandache function; Diophantine equation.