# Diophantine equation

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Particle swarm optimization based diophantine equation solver.

The Diophantine equation (11) determines only the polynomials R and S.

The Diophantine equation has two solutions called solution 1 and solution 2.

The final theorem was not formulated all the time (not even with teachers), because other important aspects needed to be clarified (such as the sieve method for counting, or the properties of the linear diophantine equation, including the existence of positive solutions), but all the activities had very substantial mathematical content, and this content was developed along the questions posed (or difficulties faced) by the participants.

v]) the v-th solution of the Diophantine equation (2), ([x.

Since p [equivalent to] 1 (mod 4), the Diophantine equation [x.

Putting everything together, we get that the number of primes p [member of] (X/2, X) such that the Diophantine equation (1) can have a non-trivial proper solution is

In this communication, the quartic Diophantine equation with three variables represented by 2[x.

It asks whether there is a mechanical procedure, such as could be programmed into a computer, for deciding whether a Diophantine equation has solutions (a Diophantine equation is one like the Fermat equation [x.

Hence, we investigate an alternative algorithm to solve an integer resource allocation problem in terms of its isomorphically equivalent Linear Diophantine Equation (LDE).

Once the desired closed-loop characteristic equation is determined, the controller polynomials R(z), S(z) and T(z) can be obtained by solving Eq 9, which is known as the polynomial diophantine equation.

1), we can simplify the resulting equation to the linear Diophantine equation shown in Eq.

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