Spock: But again Feinstein's argument would not apply to this Diophantine equation
, precisely because this Diophantine equation
can be reduced via the Euclidean algorithm to the equation,
Both methods, the standard PSO algorithm and the proposed modification PSO + GI algorithm, are tested on the Diophantine equation
solver task (see Table 1 in Section 5.
By solving the Diophantine equation
(11), the polynomials R and S can be obtained.
By Diophantine equation
, we mean that Pythagorean triples a,b,c have been substituted with natural numbers such that for any n2, the equation (5) can be expressed as:
Since Peter had stumbled across 33 + 43 + 53 = 63, I looked for other solutions to the Diophantine equation
Some groups considered equation (1) as a diophantine equation
, determined all non-negative solutions and proved that these solutions are not realisable.
The general solution of the Diophantine equation
The only solutions to this Diophantine equation
are x - x' = sa + bt, y - y' = sb - at for t [member of] Z.
In , Stroeker investigated the Diophantine equation
Hence we can write the equation 4n+8=2p as 4n - 2p= - 8 which is nothing but a diophantine equation
We search for nonzero integral triples (x, y, z) satisfying the quartic Diophantine equation
Although the phrases step function and Diophantine equation
will not come up at the elementary level, it is important for elementary mathematics teachers to lay the foundation in preparation for when students do learn about such topics.